Training a 4B model to produce 81% faster query plans than Postgres

What follows is a breakdown of an experiment I ran to explore the question: can a small, open-weights model be post-trained via supervised fine-tuning (SFT) and agentic reinforcement learning (RL) to produce Postgres query plans that beat Postgres’s default plans?

The answer to our question is a resounding yes. Highlights include:

• Attaining a 44.7% latency reduction across 113 join-heavy queries from a 4B model initially unable to produce a query plan for 99 of them
• Constructing a Postgres measurement rig that minimizes Linux page cache contention noise across concurrent containers
• Designing a custom GRPO variant for scoring RL rollouts in an inherently noisy environment
• Splitting RL across two machines: vLLM and the trainer on a rented 2x H100 node and four Postgres containers running on my desk
• Running off-policy distillation across half a thousand GPT-6 Astra agent trajectories

Let’s start from the beginning.

Inside a query optimizer

Consider the following slice of the IMDb dataset:

-- An IMDb title (movie, series, episode, etc.) [~1M rows]
title (
  id              integer PRIMARY KEY,
  title           text,
  production_year integer,
  kind_id         integer -- FK -> kind_type
)
-- Movie <> company junction table [~2M rows]
movie_companies (
  id              integer PRIMARY KEY,
  movie_id        integer, -- FK -> title.id
  company_id      integer, -- FK -> company_name.id
  company_type_id integer, -- FK -> company_type.id
  note            text
)
-- A company's name, origin, etc. [~100k rows]
company_name (
  id           integer PRIMARY KEY,
  name         text,
  country_code text     -- '[us]', '[jp]', ...
)
-- Lookup table of company roles for a title [4 rows]
company_type (
  id   integer PRIMARY KEY,
  kind text -- 'production companies', 'distributors', ...
)
-- Lookup table for what a title _is_ [7 rows]
kind_type (
  id   integer PRIMARY KEY,
  kind text -- 'movie', 'tv series', 'episode', ...
)

Let’s say I’m trying to answer the question: “Which Japanese companies put out the most titles in the 2000s?” We might write the following query:

SELECT cn.name,
       COUNT(*) AS titles
FROM   title AS t,
       movie_companies AS mc,
       company_name AS cn
WHERE  t.id = mc.movie_id
  AND  mc.company_id = cn.id
  AND  cn.country_code = '[jp]'
  AND  t.production_year BETWEEN 2000 AND 2009
GROUP  BY cn.name
ORDER  BY titles DESC
LIMIT  10;

Running this query outputs 10 Japanese companies with the number of titles they were associated with between 2000 and 2009, sorted from highest to lowest.

But how did Postgres get these results?

The path Postgres took to get this data for us is not a foregone conclusion, and it has everything to do with what we call selective predicates (i.e. the filtering conditions in a WHERE clause).

To illustrate this, let’s imagine our same query without the Japanese company filter or the date range filter:

SELECT cn.name,
       COUNT(*) AS titles
FROM   title AS t,
       movie_companies AS mc,
       company_name AS cn
WHERE  t.id = mc.movie_id
  AND  mc.company_id = cn.id
GROUP  BY cn.name
ORDER  BY titles DESC
LIMIT  10;

mc can only join with cn via mc.company_id = cn.id, and t can only join with mc via t.id = mc.movie_id.

These constraints produce two ^{There are technically eight join trees if we take commutativity into account. In this case, we don’t because it doesn’t affect the size of the relations resulting from the joins. valid join trees:}

The cardinality of a table or query result is the number of rows it contains. Assume the relevant tables have the following cardinalities:

Taking into account our joins, we get the following cardinalities:

Regardless of the order in which these three tables are joined, the same 2m rows are always passed into the second join.

Now let’s add back our selective predicates:

1. (assuming 5% of our 100k companies are Japanese)
2. (does not change)
3. (assuming 20% of our 1m titles were made in the 2000s)

The first join ordering filters the 2m movie_companies entries down to the 5% slice of companies that are Japanese. Assuming uniform distribution (we’ll discuss later why we assume this), this join results in approximately 100k rows. Joining the result with the filtered title table keeps only the 20% of those rows from the 2000s.

The second join ordering filters the 2m movie_companies entries down to the 20% slice of titles that were made in the 2000s. The same uniformity assumption holds, so the first join results in 400k rows, meaning we’re passing 400k rows into the second join.

We do 4x the work if we picked the second join ordering.

Unfortunately, it doesn’t stop there.

A combinatorial explosion

Each join can use any of:

1. Hash join
2. Merge join
3. Nested-loop join

Factoring commutativity back in now ^{While commutativity doesn’t change the number of rows produced, it must be considered now because it} does affect performance regarding the join algorithm used. , there are 4 different outer/inner join orientations, resulting in 8 possible combinations:

Lastly, each table can be scanned in different ways. Considering just four types of scans:

1. Sequential
2. Index
3. Index-only
4. Bitmap

There are 4,608 different ways to run this query ^{This is actually an undercount. Plans can run in parallel, aggregates can be hashed or sorted, etc.}

It’s also worth noting that Postgres doesn’t evaluate all of these plans. It uses dynamic programming (and a genetic algorithm for queries involving 12+ joins) to prune the search space. !

To make matters worse, every join combinatorially explodes the search space:

Estimating, not counting

Postgres is in a tough spot here. It would be reasonable to think it could simply count cardinalities and pick the plan that minimizes the number of rows passed through to successive joins.

But this would imply Postgres can count cardinalities during query planning. It can’t. In order to know this, it would need to actually run each join and count the resulting rows. This defeats the whole point of a fast query optimizer. A query optimizer does not aim to be exact in its cost minimization… it aims to be good enough across many types of queries.

Instead, Postgres uses statistics to estimate cardinalities. The planner queries the pg_statistic table, getting back common values for each column and their frequencies, and a histogram for the rest. Things get a bit more complicated when you tack on joins. Postgres doesn’t know how the rows in one table are distributed over the other. To get around this, it assumes that the frequency of a given value in the first table can simply be applied over the second table. This is the uniform distribution assumption I mentioned earlier.

Assuming a uniform distribution is fine as a heuristic, but when it fails, it fails hard. Looking back at an earlier join ordering , we filtered 2m movie_companies entries on the assumption that 5% of them were from Japanese companies. But what if the 5% of companies that are Japanese were actually responsible for 50% of the movies? The first join would produce 1m rows! The cost model says pick the first join ordering; in reality, the second one is actually better since it only sends 400k rows through to the second join.

One bad estimate in an early join can cascade through the rest of the join tree, corrupting all other estimates.

How to steer an elephant

Postgres always picks the plan with the lowest cost, and we can’t change its cost model without modifying its source code, so how can we actually steer it to pick different plans that have higher costs?

Enter pg_hint_plan.

pg_hint_plan is a beautifully simple third-party extension: just by adding structured “hints” as comments above SQL statements, you can nudge Postgres towards plans that use the instructions provided in the hint. For example:

The hint mandates usage of a HashJoin for joining pgbench_accounts and pgbench_branches, and doing a sequential scan of the pgbench_accounts table; the actual query plan follows suit nicely.

Formulating our problem

Given that we can influence Postgres to pick different—and potentially better—query plans using pg_hint_plan hints, the question we’re starting with is:

Can a language model learn to produce hints that result in better query plans?

Useful research

What might make this a worthwhile problem to solve?

My first idea was to give the model the query and the exact same set of information Postgres’s planner has. This amounts to seeing if we could build a better cardinality estimator. I came to the conclusion this is not a worthwhile avenue to explore; we would be fighting decades of cardinality estimation research. Furthermore, the inference latency alone would far outweigh any learned usefulness compared to Postgres’s ultra-fast query optimizer.

The second idea—and what I believe is the correct formulation—lies in a specific database usage pattern: heavy analytic workloads. If queries are getting run thousands of times using sub-optimal default Postgres plans, efficiency gains are being left on the table. Instead, a model could be trained to find a better way to run a specific query. The training process might require execution of that query tens to hundreds of times upfront, but the amortized cost across all runs of the query would be drastically lower.

The goal isn’t to try and beat Postgres on the time/efficiency Pareto frontier for one-off queries, but we may be able to beat it on queries that run over and over again.

A model and its harness

I decided to start with a small 4B model because it would be easiest to train/inference myself on the 2x RTX 3090 rig (affectionately named FLOPper) I have at home.

Around the time I started this project, the Qwen 3.8 family of models was released, unfortunately without a 4B variant. However, I came across a Qwen 3.8 4B distillation from a small lab in Germany called Empero and was intrigued. They used Qwen 3.8’s 2.4T model as a teacher model to distill learnings into Qwen 3.5 4B, producing empero-ai/Qwen3.8-4B-Distill. This distilled model is not outright better than its base 3.5 model; it performs better on MMLU tasks and slightly worse on GSM8K tasks. In other words, this distillation performs better when evaluated on breadth of general knowledge, and slightly worse on multi-step mathematical reasoning. As to which is better for our task, I do not know; I decided to stick with the distilled model either way.

With the model locked in, I built a lightweight agent harness, qo-agent, that would orchestrate hint production. It was given the following six tools:

1. inspect_relation — Lists a table’s columns with types and nullability, index definitions and estimated rows and bytes
2. get_column_stats — Gets Postgres planner statistics for 1-8 columns of a relation
3. get_plan — Gets the default plan’s estimates or a submitted candidate’s stored plan
4. evaluate_candidate — Validates a proposed plan action and then executes it for timing/plan diagnostics
5. keep_default — Returns Postgres’s default plan itself as the candidate and ends the search
6. finish — Takes as input a submitted candidate ID or the default plan and ends the search

To take advantage of structured outputs, the agent was instructed to produce PlanAction JSON objects. Calls to evaluate_candidate then compiled PlanAction objects into hints and prepended them to the original query.

A sample agent trajectory:

Benchmarks

An agent is useless without something to benchmark its performance against. Fortunately for us, the hard work of creating these benchmarks was already done.

The Join Order Benchmark

Leis et al. introduced the Join Order Benchmark (JOB) in How Good Are Query Optimizers, Really?. They used it to evaluate cardinality estimation and join-order optimization using our familiar IMDb dataset.

It consists of 113 queries spread across 33 query templates. Query templates differ via their relational skeleton. They reference different tables and connect them with different join predicates. You can think about them as a structural family of questions that can be answered. Queries derived from templates preserve the tables used and the join graph topology but change selection predicates.

Looking at an example:

…and here are two real queries from JOB derived from this template:

SELECT MIN(t.title) AS movie_title
FROM   company_name AS cn,
       keyword AS k,
       movie_companies AS mc,
       movie_keyword AS mk,
       title AS t
WHERE  cn.country_code = '[de]'
  AND  k.keyword = 'character-name-in-title'
  AND  cn.id = mc.company_id
  AND  mc.movie_id = t.id
  AND  t.id = mk.movie_id
  AND  mk.keyword_id = k.id
  AND  mc.movie_id = mk.movie_id;

Query 2a — “What is the alphabetically first such movie title associated with a German company?”

SELECT MIN(t.title) AS movie_title
FROM   company_name AS cn,
       keyword AS k,
       movie_companies AS mc,
       movie_keyword AS mk,
       title AS t
WHERE  cn.country_code = '[us]'
  AND  k.keyword = 'character-name-in-title'
  AND  cn.id = mc.company_id
  AND  mc.movie_id = t.id
  AND  t.id = mk.movie_id
  AND  mk.keyword_id = k.id
  AND  mc.movie_id = mk.movie_id;

Query 2d — “What is the alphabetically first such movie title associated with a U.S. company?”

The Cardinality Estimation Benchmark

Another relevant benchmark is the Cardinality Estimation Benchmark (CEB), introduced in Flow-loss: Learning Cardinality Estimates That Matter. It uses the same IMDb database and is a much larger benchmark consisting of ~13.6k synthetically generated queries organized across 16 query templates ^{CEB’s definition of a template is looser than JOB's. Two CEB templates can share the same join graph, differing only in their selectivity predicates. In JOB, every template's join graph is unique. .}

Train time, test time

Due to its size, CEB was a good fit for training the model. JOB would be used to validate the model’s performance.

You might be wondering if it makes sense to both train and test on IMDb. If it works well, hasn’t the model just learned this specific database well?

I would argue this is precisely the point. We want our model to learn IMDb well. Given our problem formulation, if this agent is continually getting used for a company’s analytic workloads across its specific databases, we need not generalize to all databases.

The real issue is making sure we’re not overfitting to JOB query templates during training over CEB. The model should learn IMDb in a way where given any query, even for structural query families it hasn’t seen before, it’s still capable of producing a good plan. In practice, this means we need to prune CEB queries that have the same shape as any of the JOB queries.

Query topology mapping

Let’s define a query’s “topology” as its structural join-graph (de-aliased table names as nodes and joins as edges). The join graph excludes all selectivity predicates; we’re only interested in joins here.

CEB queries sharing a topology with a JOB query would be removed from the training set. I wrote a small script to convert all JOB and CEB queries to their topologies and checked if there was any overlap. There wasn’t, so no filtering was required.

How to muffle an elephant

Before getting into benchmarking the agent and doing training runs, we have to talk about how Postgres was actually run, because it directly impacts the training process.

First, some facts:

• FLOPper has a CPU with 16 physical cores, 64 GB of RAM and a 2 TB NVMe SSD
• The slice of IMDb we’re using is 8.5 GB on disk
• Postgres caches pages of data retrieved during query execution into a buffer
• The operating system has its own filesystem cache doing the same thing one level down

If we run the exact same query on Postgres 20 times in a row, it won’t take the same amount of time each run. In day-to-day work, this isn’t a big deal. But the whole thesis, and the training process itself, relies on measuring whether one way of running a query is faster than the Postgres default. This means we need to do everything in our power to de-noise Postgres.

First, I needed to understand just how noisy Postgres query executions are.

I started by building a “calibration” capability into my experimentation workflow. The calibration process was simple: run Docker containers built from a Postgres image, each given a fixed slice of CPU cores and RAM to use. I set to begin; anything lower might make future training far too slow, and anything higher might lead to more CPU contention, which means more noise. Each container was given 4 cores to use and capped at 8 GB of memory.

On startup, each container initialized Postgres with identical settings and loaded the IMDb data. Calibration then opened a thread pool of size four and pushed all 113 queries onto a shared queue. Whenever a container finished measuring a query, it pulled the next one off the queue.

The actual measurement process had two phases:

1. Run the query a few times to “warm it up”
2. Then run the query 20 more times and record each execution time

So what does it mean to warm a query up? We need to bust out some OS fundamentals to understand.

Whenever Postgres executes a query, it asks the operating system (in our case, Linux) for pages of data. Linux first checks its own filesystem cache, the page cache. If the pages are present, Linux sends them over; else it reads them from disk, stores them in its cache and then sends them over. Postgres, in turn, keeps received pages in its own shared_buffers cache for easy reuse. When shared_buffers begins to overflow, Postgres evicts pages. If it needs those pages again, it must ask Linux once more.

Every time there’s a cache hit in shared_buffers for a page, Postgres increments a counter called “shared hit blocks” (SHBs). If it has to ask Linux, it increments “shared read blocks” (SRBs).

Postgres conveniently reports both counters if we run EXPLAIN with the BUFFERS option. For example, running EXPLAIN (ANALYZE, TIMING OFF, BUFFERS, FORMAT JSON) outputs something like:

{
  "Plan": {
    "Node Type": "Aggregate",
    "Shared Hit Blocks": 1800786,
    "Shared Read Blocks": 52990,
    ...
  },
  "Execution Time": 189.2,
  ...,
}

These counters give us some notion of the “warmness” of a query. After each warmup run, we compared its hit and read counts to the previous run’s. If both were within 2% of each other (and the plan hadn’t changed), we called the query warm and started measuring. A query needed at least two warmups to have something to compare, and was cut off at five regardless. The idea was that if the counters stopped moving, the data could be considered settled and cache churn would be minimized during the 20 measurements.

I set shared_buffers to a conservative 128 MB and ran the first calibration:

Half the queries were declared warm after only two runs. Not bad… at least until I dug deeper. The SRB counts weren’t dropping to zero; rather, they were hovering steady at some large number. With only 128 MB of shared_buffers against an 8.5 GB database, Postgres was consistently missing its own cache on every execution and asking Linux for more pages. “Stable” did not mean “resident.”

Linux’s page cache is fast, so this isn’t the end of the world. Unfortunately, a new problem emerged when I actually looked at the 20 measurements taken for various queries. Let’s look at one query in particular, job-13b:

14 of the 20 landed between 186 and 204 ms. The other 6 landed between 227 and 253 ms, somewhere between 14% and 26% slower. The query wasn’t even uniformly noisy, it just had two different speeds at different times, and a third of the time it ran at the slower speed.

I initially wanted to quantify noise using the coefficient of variation:

The CV tells us the “wobble” of a measurement. If a query takes 100 ms and has a CV of 5%, we could say it wobbles by about 5 ms. For job-13b, the CV was 10.3%. It wasn’t great. CV is also not a great measurement to use here. Because it’s built on the mean, it’s easily influenced by a few outlier runs.

We don’t actually care as much about how spread out the 20 runs are. We do care about how often this causes our measurement criteria during training runs to get fooled.

To fool an agent

Bear with me here as I skip ahead a little bit in order to provide more color on what exactly we needed to measure.

To de-noise during actual agent runs, I couldn’t just run the agent’s proposed plan a single time. Instead, I ran three interleaved (candidate, default) pairs sequentially. Three was picked somewhat arbitrarily to provide some measure of variability while being small enough to prevent agent evaluation runs from spending most of their time in Postgres. Once the three candidate/default execution time tuples were obtained, the medians of both the three candidates and the three defaults were taken and expressed as a ratio of each other to determine the final speedup or slowdown. If the two medians differed by less than an arbitrarily declared 5%, it was a tie. Outside of that tie zone, a candidate could be declared as a speedup or a slowdown.

Now let’s go back to our earlier job-13b example. We had 14 executions in one clump, and 6 in another slower clump. The median of three strategy sounds good until you realize that if, in theory, at least two of the three measurements landed in that “slower” clump, the median would bias towards the less frequent slower clump.

Imagine a candidate plan that executes identically to the default. No real difference exists, so the correct reward is zero. Draw three timings for the “candidate” and three for the “default” out of the 20 we observed. There are ways to draw three from 20; for job-13b, 230 of them contain at least two slow runs, so one side’s median lands in the slow clump ~20% of the time.

That’s a totally phantom 14-26% speedup or slowdown that we would show to our model as signal ~20% of the time. Dangerous!

So we can’t just rely on CV as the golden number to minimize, as two queries with the exact same CV can fool the measurement reward at different rates depending on whether the spreads are a uniform blur or two clumps sitting more than 5% apart. The actual number to minimize is this fooling rate itself.

I wrote a small script to compute the fooling rate directly from raw calibration data. It worked by sliding a window of six sequential runs across the 20. For each window, we took interleaved pairs of size two to represent an interleaved (candidate, default) pair. A window of size six gives us pairings like: (t1, t2), (t3, t4), (t5, t6). In any given pair, and can alternate roles of being the candidate query, or the default query. That means for each pair, there are two possibilities, and therefore for each window of three tuples, there are possibilities. 20 measurements means we’ll slide this window 15 times, so we have total possibilities ^{Each possibility is a binary value indicating whether or not that specific, simulated formulation of candidate/default pairs resulted in a ratio of medians between the two greater than the 5% tie-zone. for a given query.}

We derive two metrics from these raw numbers. First, we calculate the no-op error rate for a given query as the ratio of the 120 simulated possibilities that do differ by more than 5% against the number that don’t. We sum these percentages up across all 113 JOB queries and then divide by 113. This number, which we’ll call the “mean no-op error rate,” gives us the percentage likelihood that the reward may get fooled for any JOB query when doing our three paired measurements strategy. Second, we sort the no-op error rates for all 113 queries, lowest to highest. The number that is 90% of the way to the end of this sorted list is reported as the “p90 query,” and gives us a measure of the fooling rate for the worst-offending queries.

At 128 MB for shared_buffers and four concurrent containers, the “fool rate” script produced the following mean no-op error rates and p90 query numbers ^{I ran the calibration twice per config to provide a sense of how much two runs may disagree with each other. :}

The numbers aren’t good. One in twenty no-op plans get rewarded, and one in ~10 queries gets fooled more than 13% of the time.

We can do better.

Tuning Postgres

I focused on two memory-related settings Postgres exposes:

1. shared_buffers decides how much of the database Postgres can keep in its own cache
2. work_mem decides how much memory a single sort/hash operation can get before spilling to disk

I ran four calibrations:

Surprisingly, work_mem had no effect on noise at all, and shared_buffers carried all of the weight!

With 2 GB of shared_buffers, the median query ended warmup with its SRB counter at exactly zero: its working set was fully resident in Postgres’s own cache. The no-op error rate dropped by roughly 4x, and the 90th percentile query went from being fooled 13%–20% of the time to almost never. Our two-clump query, job-13b, went from a CV of 10.3% to 0.9%, with all 20 runs landing within 7 ms of each other.

One neat benefit emerged that I wasn’t initially chasing: the default plans themselves got faster. The summed runtime of all 113 JOB queries fell from 95 seconds to 60 seconds, just from cache residency. In other words, actually taking our measurements for both candidates and defaults would now be significantly faster, meaning the training process would take less time.

I locked in 2 GB shared_buffers and 4 MB work_mem for the rest of the project.

Baselines and metrics

I used two metrics for benchmarking agent performance.

Geometric mean speedup

The geometric mean speedup gives all queries equal weight. For example, in a two-query sample, if query 1 runs 2x faster than its baseline, and query 2 runs 0.5x faster than its baseline, then . It doesn’t matter if query 1’s baseline took 5 minutes and our candidate took 2.5 minutes, but query 2 only regressed from 25s to 50s, as they are equally weighted.

Total workload speedup

Total workload speedup treats the entire query set as one batch. We simply add all the baseline times and divide by the sum of the candidate times. In our above example, .

Both metrics tell different stories. The total workload speedup is a measure of practicality. A data analyst building out a suite of analytics queries wants to decrease the overall runtime across the batch. But from a model training standpoint, the total workload speedup could be entirely influenced by a single query plan the agent chanced upon; the rest of the batch could be degenerate. This implies the model hasn’t actually learned anything interesting; it just got lucky. Because the geometric mean speedup cares not for absolutes, it gives us a measure of actual learning across the batch: values above 1x imply that the average query is executing faster.

A frontier intelligence control

Before running the untrained 4B model through the qo-agent harness, I wanted to validate this problem was actually solveable by today’s frontier models. If a model like GPT-6 Astra or Qwen 3.8 2.4T couldn’t improve upon the default Postgres query plan, I couldn’t really expect the 4B model to either.

I took a small sample of 10 JOB queries and benchmarked them on both Astra and Qwen 3.8 2.4T running through the qo-agent harness:

Evaluations of Astra and Qwen 3.8 2.4T run on the same slice of 10 JOB queries. The frontier models were benchmarked at different candidate numbers (i.e. how many candidates they were allowed to generate during a complete trajectory; either a single candidate or 5) and for Astra, whether reasoning summaries ^{I was a little surprised to see Astra performance worsen with reasoning summaries on compared to the 5-candidate evaluation done right before it, but these evaluations were only run a single time on a small 10-query slice of JOB, so I chalked up the worse results to random variance. were enabled or not. Astra was inferenced through OpenAI’s API, and Qwen 3.8 2.4T through Modal via OpenRouter.}

Given the difference between the single-candidate scores and the 5-candidate scores, the agent was clearly capable of doing in-context learning across sequential executions of its candidates. This gave me the confidence to stick with an agentic multi-turn approach rather than try and train the 4B model to get really good at one-shotting a plan.

During a run of the agent, each candidate was warmed once and then measured once. After exhausting the candidate attempts budget, the model was only presented with a single tool to call, finish, and the model was told to select the best scoring candidate (or keep the default plan). After the candidate was selected, three interleaved (candidate, default) pairs were run and passed through a clipper:

The clipper constrained the result of the division between the two medians to be between . These clipper values were picked somewhat arbitrarily; I found they prevented the geometric mean speedup from getting overly influenced by an extreme speedup or an extreme regression.

Conclusion: frontier intelligence is capable of agentically doing query optimization.

The vanilla 4B baseline

We’re now ready to evaluate the untrained 4B model on JOB and see how it does!

The same 5-candidate plan budget per agent trajectory configuration was employed. The results were dismal:

Only the last three rows contribute to the score, leaving 15 valid trajectories out of 113. Nine of those 15 result in a score of 1.00x by construction (the plan was identical ^{A candidate plan was determined to be equal to the default plan if their} EXPLAIN outputs with cost and row estimates stripped were equivalent. to the default, or the model chose to keep the default). That left just six candidate plans that were:

1. Structurally intact (the PlanAction the model produced was successfully compiled into a hint comment)
2. Valid (the resulting hint was actually valid given the schema)
3. Novel (the resulting plan was distinct from Postgres’s)

Five of the six plans resulted in speedups of 1.02x–1.30x, and one of them landed at 0.05x.

The most common issues seen were:

• The PlanAction was not a valid object
• Join trees did not contain every relation exactly once
• Actions were wrapped in an extraneous action key
• LeadingLeading trees ended up being quite an important concept, as these are used to influence the join-ordering, which as we mentioned previously, is an NP-hard problem. trees had subtrees that were not actually connected in the query’s join graph
• The model called specific tools at the wrong time, or called tools that didn’t exist

Not only was the model terrible at this task, it couldn’t even grok the harness wrapped around it either.

Off-policy distillation via supervised fine-tuning

I first needed to get the 4B model to speak the “language” of the qo-agent harness. I would make it good at query optimization after.

We can use supervised fine-tuning (SFT) to do this. Specifically, we can do off-policy distillation.

Off-policy distillation is a training method by which a student model (sometimes referred to as a policy) learns to imitate outputs produced by a teacher model. It’s called “off-policy” because the training data is not generated by the student model/policy itself. It’s remarkably simple. A complete teacher trajectory (sometimes referred to as a demonstration) is shown to the student model. For every token in the trajectory, the probability the student model gave to generating that token results in a per-token loss. Averaging these per-token losses leads to a demonstration-level loss. Standard backpropagation via chain rule then lets you compute gradients for all trainable parameters in the student model, and the configured optimizer can nudge parameter values in a way where loss gets minimized in a single pass.

What’s super neat about off-policy distillation is that we don’t need a lot of data for it to work well. Because each demonstration provides us thousands to tens of thousands of token predictions, our student model’s weights adapt quickly.

How do we actually get these demonstrations though? We could write them all by hand, but that would take far too long. One step up would be writing a tool to randomly generate valid-looking trajectories ^{Fun fact: I tried this initially. It actually works decently and was able to teach the 4B model the harness. However, it caused a bunch of other issues, mostly around making the model less likely to generate novel candidate plans. . But these ignore that we have the best teacher of all already available: smarter, larger models.}

The strategy is simple: generate a bunch of trajectories by running a smart model through the qo-agent harness, and distill those trajectories into our student 4B model.

Rendering, loss masking, and unrolling

There are a few complexities to unpack.

Imagine we decide to use GPT-6 Astra as our teacher model. It produces trajectories in OpenAI’s Responses API format. Our Qwen model doesn’t understand this format; we need to transpile the human-friendly Responses API JSON format into a model-friendly token format. This is where the concept of rendering comes in. Rendering libraries can take in a trajectory’s text and convert it to a raw sequence of tokens a specific model actually understands.

Another consideration with agent trajectories is determining which tokens our model should actually be predicting. The model never produces certain tokens in a trajectory, like the system prompt, any user prompts or the results of a tool call after a harness executes it. The model should still see these tokens when predicting the next token though; they’re still part of the context, but we should only compute losses for tokens the model is responsible for predicting. We can employ a strategy called loss-masking here. A loss-masking library lets us label the parts of a teacher trajectory that are context-only, versus the parts our student model is responsible for predicting.

Finally, when fine-tuning over agent trajectories, we generally don’t include the entire trajectory as a single trainable unit. Instead, the trajectory is broken up into a set of (context, reply) pairs. The context in these pairs is additive and includes previous model replies.

Low-rank adaptation (LoRA)

Our 4B model has 4.66 billion tunable parameters. If we wanted to update all of these parameters in a single pass during SFT, we would need a GPU with at least 64 GB of VRAM. I wanted to test my hypotheses first on my consumer-grade RTX 3090s, each of which carries 24 GB of VRAM, so I needed something more parameter-efficient here.

Low-rank adapters, or LoRAs, are the canonical way to do this. At a high-level, they work by freezing the model’s weights as they are, instead letting you train a much smaller pair of matrices that when multiplied together, result in an adjustment to selected weights in your original model.

4.66 billion weights come in at 9.32 GB in bf16. The tiny LoRA I actually ended up training was only 42.5 MB and contained only 21.2 million trainable parameters.

Teacher model selection

We previously learned that frontier models could operate well in qo-agent; the next decision was picking between GPT-6 Astra or Qwen 3.8 2.4T.

Let’s look back at the results from evaluating both models on 10 JOB queries, this time zooming into context length in tokens:

The same five-candidate evaluations over the 10 JOB queries mentioned earlier, this time measured by how much context each trajectory consumed.

It seems like Astra wins on all fronts. However, Astra’s biggest drawback is that when run through the API, reasoning tokens aren’t supplied. Instead, the API gives you a short summary in place of reasoning tokens. On the other hand, Qwen 3.8 2.4T is an open-weights model and is happy to provide all of its reasoning tokens.

I was wary about training off of trajectories containing only reasoning summaries. The How to Steal Reasoning Without Reasoning Traces paper talked about this exact thing: training off reasoning summaries resulted in the student model’s performance decreasing. To combat this, the authors devised a new method: trace inversion. Trace inversion calls for synthetically expanding a reasoning summary into what the raw reasoning tokens may have looked like. Although they’re not exactly the ones Astra actually produced during inference, the longer reasoning blocks led to improved performance when transferred over to a smaller model. This provided some level of comfort; if I picked Astra and performance suffered, I could experiment with trace inversion.

The other consideration was context lengths. Given I was only doing SFT off a single RTX 3090 to start, I needed any given trajectory to not exceed ~50k tokens in sequence length. If it did, the training process might OOM given the 3090’s limited 24 GB of VRAM. All Astra trajectories fit under that budget, but some of the Qwen 3.8 2.4T ones didn’t.

I decided to try out SFT on the Astra traces. If performance suffered, I could explore trace inversion; if that didn’t work, I could rent beefier GPUs for training, bump our global context limit, and use Qwen 3.8 2.4T traces instead.

I began by generating 120 Astra trajectories over a random slice of queries from CEB, with reasoning summaries enabled. 100 trajectories would be used for training, and 20 would be used as a held-out validation set. All trajectories were rendered via Prime Intellect’s renderers library into Qwen format, loss-masked appropriately and unrolled and packed into usable training demonstrations. I then used Prime Intellect’s prime-rl library to run SFT, training the smaller ~21 million parameter LoRA. 100 Astra trajectories became 382 training rows after unrolling and packing. I allowed training to run for just a single epoch, meaning every example was trained on exactly once, and used a batch size of one (each demonstration updated the weights). Finally, I evaluated the resulting LoRA over JOB:

The one-epoch adapter against the untrained model on all 113 JOB queries. A query counts as scored when its trajectory ended with a measured candidate, a duplicate of the default plan, or the default itself. Wins and regressions are scored queries more than 5% faster or slower than the default.

Promising! The adapter learned the harness.

I could now either generate more fresh trajectories, or do more epochs over the dataset we already had. Given the latter is cheaper, I decided on more epochs.

It was around this point that I got impatient and wanted the training process to run even faster, so I rented a 2x H100 node on Lambda.

Now training on an H100 ^{Switching to the H100 meant we had 80 GB VRAM at our disposal instead of 24 GB. We could have bumped the context token limit greatly, but I decided to barrel through with the roughly ~50k token limit we set. instead of a single RTX 3090, I did two more training runs} ^{Training runs were a lot faster on the H100. The first epoch took four hours on the RTX 3090; the second took only 45 minutes on the H100. over the existing LoRA; a second epoch and then a third:}

Two and three epochs over the same 100 Astra trajectories, evaluated on JOB. Before epochs two and three, the qo-agent harness was upgraded to allow the model to keep the default plan after a search, which is why many more queries are scored. The two- and three-epoch rows were evaluated under identical settings.

Two epochs improved our results, but three epochs regressed them! This was especially interesting because validation loss didn’t budge at all during the second epoch:

A very good lesson that a flat validation loss doesn’t necessarily mean the model has stopped learning useful behavior.

I still felt we had more to learn from SFT though before proceeding with RL. I did zero filtering on the training trajectory dataset, and hadn’t carefully audited if I was missing any capabilities. It turns out I was, mostly around the model’s ability to construct valid Leading trees.

I generated another 320 Astra trajectories; 300 for training, and 20 for validation. I filtered out just six training trajectories where Astra opted to keep the default plan without even trying a single candidate. I did two more epochs in two separate runs:

Continuing the two-epoch adapter on the 300 new trajectories, evaluated on JOB.

Our 4B model not only learned the harness; it was now genuinely making good calls on various JOB queries! Fortunately, training on reasoning summaries didn’t harm performance.

Making the 4B model good at query optimization

The model now spoke the “language” of the qo-agent harness, and we got some free performance gains out of SFT too. It was time to make it very good at query optimization.

Agentic reinforcement learning

Agentic RL differs from SFT in that we actually run the current policy over training queries inside the agent harness times. Each run (also referred to as a rollout) results in a final output that’s scored against some verifiable criteria. Lastly, each rollout’s score is then weighted relative to the other same-query rollouts. A positive “advantage” is reinforced by making the model’s weights more likely to produce that trajectory in future runs, and a negative advantage is penalized; the weights are updated to be less likely to produce that trajectory in future runs.

Designing per-rollout rewards and relative advantages

The initial reward algorithm was simple:

The speedup was calculated as the median of three default plan measurements divided by the median of three candidate plan measurements.

For every evaluated candidate that was invalid, we subtracted 0.1 from the natural log of the speedup ratio. We subtracted a further 0.05 if the rollout resulted in a plan that shared the same fingerprint as the default Postgres plan. Finally, if the trajectory ended with no valid candidate at all, a flat 3 was subtracted from the reward in lieu of any of the 0.1 or 0.05 subtractions.

The first few RL runs I did using this reward resulted in a model that was terrified of producing invalid plans due to the extremely harsh -3 condition. The model played it safe instead, returning Postgres’s default plan over and over again, accepting the smaller 0.05 reward hits.

GRPO exacerbated this issue. The plain GRPO algorithm converts multiple rollout rewards into relative “advantages”:

Let’s say we perform four rollouts for a given query resulting in the following plans, execution speeds and rewards:

We’re reinforcing bad behavior by telling the model it’s okay to produce plans that end up being equivalent to Postgres’s default plan!

Both the busted reward algorithm and GRPO needed to be swapped out for something that could actually score advantages relative to the default plan’s execution time.

The reward was updated as follows:

Changes include clipping the speedup ratio to bound scalar reward values, soft-thresholding by 0.05 to account for measurement noise, and scoring zero if the agent called keep_default or finish(default). Trajectories ending without a valid candidate incurred a flat 0.1 fee instead of the previous 3.0, and candidate plans that fingerprinted to the default plan accrued small 0.02 fees.

prime-rl-flavored GRPO was swapped out for a custom “anchored” variant:

Let’s take a look how our modified GRPO performs under the same four rollouts demonstrated above:

The modified GRPO successfully applies a negative advantage to all four of these poor rollouts, down-weighting their likelihood across the board.

Training commences

With the reward and relative advantage model locked in, I could begin training…

…as soon as I built out a mechanism for Postgres measurements to happen on FLOPper and training/inference to happen on the 2x H100 node. I would have loved to keep Postgres measurements on the Lambda node; alas, I ran a bunch of Postgres calibrations on their boxes and am reasonably confident I was sharing the non-GPU bits of the box with other folks, as the noise was off the charts compared to FLOPper.

I connected FLOPper to the Lambda node via Tailscale; the resulting process would be:

1. Query rollouts would begin on FLOPper and hold an available Postgres container for their full lifetime
2. The rollout would do inference via vLLM running on the first H100 to generate a trajectory
3. All measurements were run on the held Postgres container
4. Finally, rollout results were sent to the second H100 to compute relative advantages and update weights

Now training could start. I began by merging the final SFT adapter into the base model, creating a new base model in the process, and initialized a new adapter for RL training.

I started with an extremely conservative learning rate of 1e-06, a batch size of 8, four rollouts per query, and did just 120 optimizer updates to prove out the mechanism.

The trained LoRA was evaluated against JOB, and completely flopped:

The first RL checkpoint against the SFT checkpoint it started from, evaluated on all 113 JOB queries.

Either the reward design wasn’t good, modified GRPO wasn’t working, or we simply weren’t being aggressive enough.

The latter was easiest to test. I increased the learning rate one order-of-magnitude from 1e-06 to 1e-05, bumped the batch size to 16 and the number of rollouts per query from four to eight, and decided to do 600 optimizer updates instead of just 120.

Around this time, I learned that for a rollout, 92% of the rollout’s time was spent in vLLM inference! Given the increase in the number of optimizer updates, I needed to be smarter about this.

I refactored the training process so that rollouts leased an available Postgres worker only for the times where measurements were needed. Because of this new async approach, I could saturate vLLM and the trainer much further, and was able to run 20 rollouts concurrently, each contending for the same four Postgres workers.

I ran two stacked 600-optimizer update RL runs, back-to-back. The share of rollouts earning positive advantages steadily increased:

And the results from both checkpoints against JOB:

Both 600-update checkpoints against the SFT checkpoint they descend from, evaluated on all 113 JOB queries.

The valid candidate rate rose nicely, alongside both the geometric mean speedup and total workload speedup!

I ran the final RL checkpoint against JOB again, this time doing three rollouts per query instead of just one. In other words, each query could produce up to 15 candidates max, and the best-of-15 was picked for each query ^{This is roughly how I would expect someone trying to tune a workload of queries to use a model specially trained on this task. They would care more about the best candidate possible sampled from many rollouts, rather than just a single rollout. :}

The final 1,200-update RL checkpoint with three trajectories per JOB query. The first row averages the model’s own final selections over all 339 trajectories. The second applies a fixed rule within each trajectory, choosing the candidate with the best preliminary feedback if it beat 1.05x and the default otherwise. The third applies the same rule across a query’s three trajectories, so each query gets one answer chosen from up to 15 candidates.

When taking the best feedback across three rollouts, we saw a 1.81x geometric mean speedup, and coincidentally a 1.81x total workload speedup too.

What the model learned

After all this training, what did the model actually learn?

Costs

This project would have been free ^{Barring the price of electricity for continually running FLOPper when both GPUs were fully utilized, which at current rates costs about ~$9/day. had it not been for my impatience to get training results faster} ^{“What about the Astra traces?,” you might ask. I did not experiment with it, but I do think the 4B model could have eventually learned the harness language through just RL alone, as DeepSeek-R1-Zero showed. It might have just taken} a lot more rollouts. . I paid ~$800 to rent a 2x H100 SXM node from Lambda for ~95 hours, and ~$400 in OpenAI API fees to generate the Astra trajectory demonstrations.

Total cost: $1,200.

Conclusion

Via off-policy distillation and reinforcement learning, a tiny 4B model went from not being able to understand the harness it was wrapped in, to achieving a 1.81x geometric mean speedup and a summed latency decrease of 44.7% across a workload of join-heavy SQL queries ^{Given three attempts per query in a best-of-15 measurement, as previously mentioned. .}

It’s easy to take tiny models for granted when 5T+ parameter behemoths exist. We shouldn’t.

Frontier intelligence is extremely powerful; the distillation I did off Astra trajectories is proof enough that large models are not going anywhere.

But I do believe this experiment proves out a hypothesis many companies are waking up to: they have the data; it’s not a far-cry to build out an RL environment and spend a small sum to train and inference open-weights models on niche, domain-specific tasks. I think small models will be increasingly used for this, as they are faster and cheaper to train.

I architected the infra/training stack myself plus used my own GPUs as a learning exercise, but there are a growing number of out-of-the-box solutions for companies to easily train their own models.

I’m personally very excited to see how this space continues to grow!

Next steps

As for what I’d want to try next, just a few ideas:

• Explore whether structured hint sweeping in the style of Bao: Learning to Steer Query Optimizers is more effective than using a 4B model
• Attempt on-policy distillation and compare performance against off-policy distillation
• Try trace inversion and see how it influences off-policy distillation
• Measure “fooled reward” noise on dedicated EC2 boxes to understand how this experiment could be scaled up

Acknowledgements

I did this research while on sabbatical at the Recurse Center. Many thanks to the folks here who helped inspire this research direction!

Code

All code for this project is available here.

Citation

Please cite this work as:

Bansal, Rohan. “Training a 4B model to produce 81% faster query plans than Postgres”. rohanbansal.com (Sep 2026). https://rohanbansal.com/qorl Or use the BibTeX citation:

@article{bansal2026qorl,
  title = {Training a 4B model to produce 81% faster query plans than Postgres},
  author = {Bansal, Rohan},
  journal = {rohanbansal.com},
  year = {2026},
  month = {September},
  url = "https://rohanbansal.com/qorl"
}

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