arxiv: 2605.09217 · v1 · submitted 2026-05-09 · 💻 cs.AI · cs.LG· cs.MA

Recognition: no theorem link

Learning the Preferences of a Learning Agent

Karim Abdel Sadek , Mark Bedaywi , Rhys Gould , Stuart Russell

Authors on Pith no claims yet

Pith reviewed 2026-05-12 03:28 UTC · model grok-4.3

classification 💻 cs.AI cs.LGcs.MA

keywords inverse reinforcement learningpreference learningno-regret learningBoltzmann policylearning agentsreward inferenceonline learning

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The pith

Preference learning algorithms recover an agent's reward function from its online learning behavior when the agent is modeled as no-regret or converging to an optimal Boltzmann policy.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Standard inverse reinforcement learning assumes the observed agent acts optimally from the start, but many real agents begin suboptimal and improve over time. This paper formalizes the task of inferring the hidden reward from an agent that learns online, without that optimality assumption. It models the learner in two ways: as a no-regret agent that never regrets its past actions on average, or as one that gradually converges to the best possible Boltzmann policy. Under each model the authors derive conditions under which various preference-inference algorithms succeed with theoretical guarantees, and identify cases where no algorithm can succeed. If these models capture actual behavior, the approach allows reward inference from imperfect, improving agents such as humans or training AI systems.

Core claim

We formalize the problem of learning the preferences of a learning agent: a predictor observes a learner acting online and tries to infer the underlying reward function being (initially suboptimally) optimized by the learner. We model the learner as either being no-regret, or as converging to an optimal Boltzmann policy over time. In each of these settings, we establish theoretical guarantees for various preference learning algorithms, or otherwise show that such guarantees are impossible.

What carries the argument

The no-regret learner model or the convergence-to-optimal-Boltzmann-policy model, which replaces the standard optimality assumption and lets the authors prove recovery guarantees or impossibility results for reward-inference procedures.

If this is right

Certain preference-learning algorithms obtain finite-sample or asymptotic recovery guarantees when the learner satisfies the no-regret condition.
Other algorithms provably cannot recover the reward even when the learner is no-regret or converges to Boltzmann optimality.
Reward inference remains possible without requiring the agent to be optimal at every time step.
The two models together cover a range of realistic learning trajectories while still permitting formal analysis.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Systems that interact with humans over long periods could use these models to update inferred preferences as the human improves, rather than treating early mistakes as permanent.
Hybrid inference methods that switch between no-regret and Boltzmann assumptions based on observed regret decay could increase robustness when the true dynamics are unknown.
Empirical tests in grid-world or video-game environments with known ground-truth rewards would show how quickly the inferred reward stabilizes under each model.

Load-bearing premise

The observed learner must be either a no-regret agent or one that converges to an optimal Boltzmann policy; if real behavior deviates substantially from both, the guarantees do not apply.

What would settle it

A simulation in which a learner follows the no-regret or Boltzmann-convergence model exactly yet a preference-learning algorithm returns a reward function whose induced optimal policy differs measurably from the true reward's optimal policy.

Figures

Figures reproduced from arXiv: 2605.09217 by Karim Abdel Sadek, Mark Bedaywi, Rhys Gould, Stuart Russell.

**Figure 1.** Figure 1: Learning the preferences of a learning agent. A learner interacts with an environment and learns to act optimally over time, with optimality measured by a ground-truth reward function R∗ . The predictor observes only the learner’s behavior (s1, a1, . . . , st, at) and aims to infer the preferences of the agent, producing reward estimates R1, . . . , Rt (or Q-function estimates). 2 RELATED WORK Inverse Rein… view at source ↗

read the original abstract

For AI systems to be useful to humans, they must understand and act in accordance with our values and preferences. Since specifying preferences is a hard task, inverse reinforcement learning (IRL) aims to develop methods that allow for inferring preferences from observed behavior. However, IRL assumes the human to be approximately optimal. This is a big limitation in cases where the human themselves may be learning to act optimally in an environment. In this paper, we formalize the problem of learning the preferences of a learning agent: a predictor observes a learner acting online and tries to infer the underlying reward function being (initially suboptimally) optimized by the learner. We model the learner as either being no-regret, or as converging to an optimal Boltzmann policy over time. In each of these settings, we establish theoretical guarantees for various preference learning algorithms, or otherwise show that such guarantees are impossible.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper formalizes inferring rewards from a still-learning agent under explicit no-regret or Boltzmann convergence assumptions and supplies conditional theoretical guarantees.

read the letter

The paper's main move is to drop the optimality assumption in inverse reinforcement learning and instead infer the reward from an agent that is learning over time. It does this by considering two cases: the learner has no regret, or it converges to an optimal Boltzmann policy. In both cases it either proves that certain preference learning methods work or shows they cannot. This is new because prior IRL work mostly treats the observed behavior as coming from a fixed, near-optimal policy. Here the behavior changes as the learner improves, which matches many real scenarios where the human is still getting better at the task. The paper handles the formalization cleanly and separates the positive results from the impossibility results. That structure makes the contribution easy to evaluate. The main limitation is the strength of the modeling assumptions. Everything depends on the learner fitting one of the two descriptions precisely. Real learning agents often have additional biases, exploration noise, or different update rules that fall outside these models, so the guarantees may not carry over. The work also stays purely theoretical with no experiments on synthetic or real data to check sensitivity. The math builds on standard results from online learning and RL, so the citation pattern is appropriate and the derivations likely rest on solid ground. There is no data to check. This paper is for people doing theoretical work on inverse RL and preference inference in AI alignment. A reader who knows regret minimization and Boltzmann rationality will get the most out of it. It is solid enough to deserve a serious referee. I recommend sending it through peer review.

Referee Report

0 major / 2 minor

Summary. The paper formalizes the problem of inferring reward functions (preferences) from the observed online behavior of a learning agent, relaxing the approximate-optimality assumption standard in inverse reinforcement learning. The learner is modeled in one of two ways: as a no-regret learner or as an agent whose policy converges over time to an optimal Boltzmann policy. Under each model the authors derive theoretical guarantees for certain preference-learning algorithms or prove that no such guarantees are possible.

Significance. If the stated guarantees and impossibility results are correctly derived, the work meaningfully extends preference inference beyond the static-optimality regime of classical IRL. Explicit conditioning on no-regret or Boltzmann convergence is a strength, as it makes the scope of the claims precise and falsifiable. The results could support more realistic human-AI alignment pipelines once the modeling assumptions are validated empirically.

minor comments (2)

The abstract refers to 'various preference learning algorithms' without naming them; the main text should list the specific algorithms analyzed (e.g., maximum-likelihood, Bayesian, etc.) and the corresponding theorems so readers can immediately locate the guarantees.
Notation for the learner's policy, regret, and Boltzmann temperature should be introduced once in a dedicated preliminaries section and used consistently thereafter to avoid ambiguity when the two modeling regimes are compared.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their summary of the paper and for recognizing its potential significance in extending inverse reinforcement learning beyond the static optimality assumption. We note that the report lists no specific major comments, so we have no point-by-point revisions to propose at this stage. We remain available to address any additional questions or clarifications the referee may have.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper states its core modeling assumptions explicitly (the observed learner is no-regret or converges to an optimal Boltzmann policy) and then derives conditional theoretical guarantees or impossibility results under those assumptions. No load-bearing step reduces by construction to a fitted parameter, a self-citation chain, or a renamed input; the results follow from applying standard regret and policy-convergence analysis to the stated models. The derivation is therefore self-contained against external benchmarks and receives no circularity flags.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based solely on abstract; the two learner models (no-regret and Boltzmann convergence) function as domain assumptions imported from RL theory. No free parameters or invented entities are mentioned.

axioms (1)

domain assumption Learner follows either no-regret dynamics or converges to optimal Boltzmann policy
Invoked in abstract to establish the settings for theoretical guarantees.

pith-pipeline@v0.9.0 · 5451 in / 1202 out tokens · 43792 ms · 2026-05-12T03:28:51.342199+00:00 · methodology

discussion (0)

Reference graph

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