Reinforcement learning to choose optimizers

No single optimization method is uniformly best for all problems, and the most suitable optimizer choice can change during a run. Existing approaches that change optimizer during execution typically predetermine part of the strategy: the portfolio is restricted to one algorithm class, the switch occurs once at a fixed time, or the frequency of decisions is treated as a hyperparameter rather than a learned one. We introduce "Reinforcement Learning to Choose Optimizers", which formulates the optimization algorithm choice as a sequential decision-making problem. At each decision, a recurrent policy reads the current run state and decides both which optimizer should be used next and for how long. The portfolio includes both gradient-based and derivative-free optimizers, and each switch passes on the current best solution and a representative step size. A context proxy conditions a gating network over expert heads, and training employs a decoupled actor-critic whose return is expressed in the same empirical runtime distribution metric used at evaluation. Training tasks and portfolio are designed jointly so that no optimizer dominates. On unseen problems, the learned policy outperforms every portfolio optimizer at all but the smallest budgets, and it remains robust under distribution shift.

CaRL-EM: Cost-Aware Reinforcement Learning for Entity Matching with LLMs

Entity matching (EM) requires fine-grained contextual understanding and domain knowledge. Recent work shows that large language models (LLMs) can serve as strong matchers across domains, but most methods either make independent pairwise decisions or rely on manually designed composite pipelines, thus lacking flexibility in realistic multi-candidate settings. At the same time, they typically ignore inference cost at scale. We formulate LLM-based EM with candidates as a cost-aware sequential decision problem and propose CaRL-EM, a reinforcement learning controller that manages LLM operations. Given the state of an anchor record, its candidate set, and the cost, CaRL-EM adaptively chooses among different operators (Match/Compare/Select/Decide) and model capacities to maximize a quality-cost objective. The policy interacts with abstract operators, allowing the same controller to be reused with different underlying LLM backends at inference time without retraining. Experiments on 7 benchmarks show that CaRL-EM (i) learns to dynamically plan the usage of inexpensive and expensive operators based on task complexity, (ii) achieves robust zero-shot transfer across diverse datasets and domains, and (iii) consistently achieves a better quality-cost trade-off than strong LLM-based baselines and manually designed pipelines, yielding a lower inference cost at comparable or higher quality.

RetailAgent: Structured Adverse Timing in Self-Conditioned Multimodal LLM Trading Agents

In financial markets, a sequential policy that reacts systematically to price movements may become predictable to other market participants. This paper studies whether large language model (LLM) agents exhibit such directional structure through RetailAgent, an experimental framework in which an LLM observes anonymized intraday equity price histories and permitted state, then repeatedly chooses long (hold the stock) or flat (stay out) before the subsequent interval return is revealed. We compare returns during long and flat intervals along the same stock's intraday path after removing the overall fraction of long decisions. This exposure-matched measure reveals persistent negative timing across modality, horizon, state, and model family. Shuffling saved action sequences substantially attenuates the effect, showing that alignment between actions and subsequent returns drives the negative score. Feeding self-authored memories into decisions further increases policy persistence, while timing becomes more negative among stock-days on which the agent uses both actions. These results reveal stable, recoverable directional structure in sequential LLM financial decisions and a behavioral signal for studying how another participant could respond to a predictable policy.

Chance-constrained selection of sequential intervention strategies from counterfactual estimates

Many operational decisions are sequences of interventions under a cumulative resource limit, such as a maintenance schedule within a crew-hour budget. Choosing among them calls for the outcome and the cumulative cost each would produce, counterfactual quantities identified from observational data. Two strategies with the same expected cost can exceed the budget at very different rates, so constraining the mean does not bound how often an overrun occurs. Prior two-step architectures, recently extended to continuous doses, constrain the mean cost rather than its tail and allocate at a single decision point. Methods that do bound a cost tail take its distribution from a specified model rather than identifying it from data. We present a predict-then-optimize framework. In the prediction step, any estimator returning an outcome value and a cost distribution supplies what the decision rule consumes, so the predictor is interchangeable. In the optimization step, a chance-constrained selection over a finite candidate set bounds the probability that the cumulative cost exceeds the budget. That tail does not decompose across stages, so each strategy is scored whole. Sweeping the tolerated violation probability traces a safety-utility frontier, and distribution-free finite-sample bounds cover violation and outcome shortfall. Four of five environments, spanning clinical treatment and equipment maintenance, supply exact counterfactual ground truth; the fifth carries real outcomes from a digital-health micro-randomized trial. Across them, the rule holds the budget where a point-estimate rule overruns it, at an outcome cost the frontier makes explicit. All code is available at https://github.com/mfriendly/counterfactual-chance-selection

Towards a Formal Definition of Agent Memory: Basis, Span, Optimality, and the Sequential Memory Problem

Despite the wide deployment of memory in large-model agents, there is no unified formal account of what a memory is or when it is optimal. This paper takes a first step toward this account. The central idea is that memory is a basis, knowledge is its span, and answerability is a coverage problem: an agent stores events extracted from a material; a generation operator turns any event set into the knowledge it entails; and a query is answerable exactly when some single item in the span covers it. The optimal memory is then the capacity-constrained maximizer of expected coverage, and its value traces a utility--capacity frontier, the common yardstick on which memory systems can be compared. Next, we consider noise in the memory and discuss coverage versus precision under it: a memory may store false claims, so the write policy must infer the truth of what it stores. Drawing an analogy with biological memory, which is formed continuously through ongoing experience, we formalize the continual agent-memory problem in a sequential MDP that covers multiple levels, where memory is the state, writing is the action, and the utility settled at query time is the delayed reward that drives learning. To make the framework concrete, we instantiate it on Homer's \emph{Odyssey}, turning the frontier, the compression zone, and the divergence of coverage from precision into concrete numbers. Finally, we position existing systems within the framework, making ``how good is a memory'' measurable and recasting the open problems of constructing and learning agent memory as concrete research questions.

Let it Cook: Learning to Wait in Sequential Decision Making

In sequential decision making, an agent typically observes its environment and acts at every timestep. However, such active participation may not always be necessary; tasks such as brewing coffee include periods that are served equally well by letting the environment evolve without constant monitoring and control. During such periods, the agent could simply wait to conserve its resources, or redirect its attention to another task. We capitalize on these opportunities by training a "waiting policy" that decides where and how long to wait. This involves forgoing sensing to commit to a wait action, representing a deliberate pause for a set number of timesteps. We formalize "learning to wait" as minimizing the frequency of sensing and decision making without sacrificing task performance (e.g., the total amount of time to complete a task). To train a waiting policy, we propose an approach that employs reinforcement learning with lexicographically ordered objectives. In experiments across 4 discrete-state household tasks and 3 continuous-state environments, we show that our approach successfully learns waiting behaviors, and can adapt pre-trained policies to wait where appropriate. While different tasks permit different amounts of waiting without sacrificing task performance, our approach consistently finds solutions with significant waiting, sometimes waiting for over 50 percent of the task duration.

Hybrid LLM-Augmented Reinforcement Learning Agents for Complex Sequential Decision Tasks

Large Language Models (LLMs) have recently shown strong capabilities in reasoning, planning, and tool-use, enabling new forms of autonomous agents. However, LLM-based agents struggle with long-horizon sequential decision tasks that require precise action optimization and environment interaction. Reinforcement Learning (RL), while effective for sequential control, often lacks the high-level abstraction and task decomposition abilities needed for complex scenarios. This paper introduces an LLM-Augmented Reinforcement Learning Agent that integrates LLM-driven planning with RL-based action optimization. The proposed architecture leverages the LLM to generate subgoals, structured plans, and contextual guidance, while the RL agent refines low-level actions through interaction with the environment. Experiments on sequential decision tasks demonstrate improved sample efficiency, higher success rates, and more coherent action trajectories compared to RL-only and LLM-only baselines. This hybrid paradigm highlights a promising direction for building more capable autonomous systems.

BRiG-AFA: Bellman Risk-to-Go Learning for Non-Myopic Active Feature Acquisition

Active feature acquisition (AFA) asks which unobserved feature to measure next for each test instance under a budget. Greedy rules are easy to train but can overlook context features whose value is realized only through later acquisitions, while reinforcement-learning and generative approaches introduce difficult optimization or conditional-density estimation. We introduce \method, a deployable, supervised alternative that learns a separate candidate-conditioned risk-to-go function for every remaining budget. Starting from the one-step terminal classification risk, the functions are fitted backward with Bellman targets; inference greedily minimizes the learned terminal risk using only observed values, the mask, candidate identity, and remaining budget. A controlled non-myopic benchmark shows the expected mechanism: at budgets two and three, \method improves accuracy over its one-step ablation by $4.84\pm2.17$ and $4.39\pm1.10$ percentage points (mean $\pm$ standard error over five seeds). On Fashion-MNIST with 20 candidate pixels, it improves accuracy at every nontrivial reported budget on average, including $10.20\pm0.74$ points at four acquisitions; its mean paired gain across budgets $\{2,4,8,12,16\}$ is $3.50\pm0.37$ points. A three-seed MiniBooNE study is mixed at small budgets but positive at 8 and 16 acquisitions, identifying a current boundary rather than supporting a universal claim. These results establish a reproducible mechanism-level case for direct Bellman risk regression and delimit the experiments still needed for state-of-the-art comparison.

Self-Certification of Representation Adequacy: Sequential Certification at Minimum Task Loss

Agents that act on a compressed representation of their history face a structural risk: if the representation aliases histories with different optimal actions, no rule measurable with respect to the representation can avoid an irreducible per-round loss, and the agent may be unable to detect this from its own transcript. This paper develops a four-layer theory of self-certification of representation adequacy. The static layer defines decision-theoretic adequacy through a Bayes-risk grouping identity and prices a one-shot external verification by an exact total-variation threshold. The sequential layer poses certification as an optimal-stopping problem in the currency of task loss: we define an environment-wise certification complexity constant through a covering linear program, prove an information-task-loss lower bound for every delta-correct strategy, and give a Certification Track-and-Stop policy whose cost matches the bound asymptotically. A final boundary layer gives an explicit kernel-switching example and identifies the open theorem needed to cover policy switching or representation repair; it does not claim that the fixed-kernel guarantees extend to representation revision. The proofs of the two main theorems are given in full in the appendices.

AgentHPOBench: A Benchmark For Evaluating LLM Agents as Sequential Hyperparameter Optimizers

As LLMs evolve from code completion systems into autonomous scientific agents, evaluating their ability to conduct experiments has become increasingly important. Existing benchmarks typically focus on static code generation, paper replication, or final answer correctness, but do not directly assess whether agents can interpret experimental evidence and use it to guide subsequent hyperparameter decisions. To address this gap, we introduce AgentHPOBench, a sequential benchmark comprising 30 executable machine learning tasks across seven research categories. Each task begins with a validated baseline run, after which an agent performs several sequential interventions. At each step, the agent observes the accumulated configurations, metrics, and logs before proposing the next valid configuration. We evaluate 12 widely used agents and conventional HPO baselines under a unified protocol. The results show that current agents exhibit measurable experimental optimization ability across domains, but still face clear limitations in sustained iterative refinement, complex log diagnosis, and consistent progress toward reported reference performance.

Breaking Feedback-Blindness: Utility-Augmented Transformer for Sequential Decision Making

Sequential decision making in non-stationary and partially observable environments requires rapid adaptation to latent regime changes. However, existing Transformer decision models face a structural bottleneck in the retrieval mechanism: even when reward is used for training or exposed as an input token, attention retrieval remains primarily driven by observation-derived similarity. We formalize this limitation as feedback-blind retrieval, and formally show that, on feedback-informative tasks, observation-equivalent histories with different action-reward outcomes cannot be distinguished by any observation-only attention, resulting in suboptimal choice. To address this mismatch, we propose the Utility-Augmented Transformer (UAT), a new feedback-conditioned retrieval attention architecture in which a compact utility state modulates the query, key, and value projections, allowing action-reward history to directly alter context retrieval during the forward pass. UAT also enjoys an exact zero-gate degradation property that recovers the Vanilla Transformer when feedback is uninformative. Under finite-horizon compactness and Lipschitz assumptions, we prove that UAT strictly enlarges the observation-only Transformer class and can uniformly approximate feedback-dependent decision maps. Across four non-stationary benchmarks: synthetic navigation with hidden goal shifts, non-stationary sepsis treatment, cross-market portfolio allocation, and delayed-feedback recommendation, UAT consistently improves performance over observation-only, test-time adaptation, and input-level feedback baselines, with particularly large gains in noisier regimes that require stronger adaptation.

Can Induced Emotion Bias LLM Behaviors in Sequential Decision Making?

As Large Language Models (LLMs) are increasingly deployed as autonomous agents in high-stakes domains, understanding contextual factors that may modulate their decision-making becomes critical. While LLMs are trained to perceive and resonate with users' emotions, it remains unclear whether induced emotion can influence their sequential decision-making. We investigate this question using the Iowa Gambling Task (IGT), a classic psychological paradigm for studying decision-making under uncertainty, combined with an imagination-based emotion induction procedure. We first validate the feasibility of this paradigm by confirming that LLMs can sense strong, distinguishable emotions from context and that LLM agents can learn from sequential interactions in a human-like pace. With the validated setup, we find that, different from humans, induced emotion does not significantly bias the decision dynamics of LLM agents on average. However, the effects of anger are conditioned: inducing anger makes LLM agents less sensitive to penalties for bad decisions, and in early stages of the game, anger can lower exploration, locking decisions into a few choices early. These findings reveal the subtle yet distinct effects of induced emotion on LLM decision-making compared to human behavior, and provide a tool for future research on affective modulation of LLM agents.

Beyond Next-Observation Prediction: Agent-Authored World Modeling for Sequential Decision Making

Recent studies on world modeling for Large Language Model (LLM) agents typically formulate the learning objective as next-observation prediction. However, this objective ties supervision to what a transition happens to reveal, which may omit the dynamics most relevant to the agent's current decision. To bridge this gap, we propose Agent-Authored World Modeling (AAWM), a training procedure that constructs supervision from the policy's own decision needs. Specifically, at each state, the agent identifies what it needs to understand about the environment before acting. These needs drive the retrieval of relevant transition evidence across trajectories, which is then synthesized into training targets that capture decision-oriented dynamics instead of reconstructing the next observation. This aligns the training objective with the dynamics the policy needs before acting, not with the contents of the next observation. Experimental results validate the effectiveness of AAWM across multiple environments and training settings. These results show that decision-aware world-model targets provide a more effective learning signal than next-observation prediction.

Maturing Markov Decision Processes: Decision Making under Increasing Information and Shrinking Action Sets

Sequential decision problems often exhibit an asymmetric evolution of information and decision flexibility: as a decision cycle unfolds, the agent receives richer information while feasible actions expire due to operational cutoffs, commitments, or resource constraints. Standard MDP formulations typically flatten this structure into stage-dependent state descriptions and action masks, thereby obscuring the nested information--action asymmetry that determines which decisions are urgent and which can be deferred. We introduce Maturing Markov Decision Processes (MMDPs), a formulation built around this information--action asymmetry. We characterize one of its key consequences through an expiring-action priority principle, which identifies the actions that must be resolved before the next stage. Motivated by this structure, we develop a structure-aware reinforcement learning framework with stage-aware policy design, expiring-action abstraction, and search-augmented learning with distillation. Experiments on a controlled multi-supplier replenishment problem, simplified cash-management environments of increasing complexity, and a production-scale simulator show that explicitly modeling this asymmetry improves learning efficiency and becomes increasingly valuable as decision problems scale.

Stepwise Token Selection for Efficient Multimodal Large Language Models

In multimodal large language models (MLLMs), inference cost is largely dominated by the visual token prefix rather than the language backbone, making token reduction a key factor for improving efficiency. Existing approaches typically assign independent importance scores to visual tokens and retain a fixed number of top-ranked tokens, implicitly assuming token independence and a uniform compression ratio across inputs. In this work, we reformulate visual token pruning as a sequential decision-making process. Specifically, we introduce a pointer-style selection mechanism that iteratively chooses informative tokens, conditioning each decision on previously selected ones, and dynamically determines when to stop via a learned termination action. This enables joint optimization of both the selected subset and its size. To enable end-to-end training under standard language modeling objectives, we design a differentiable relaxation based on a variance-preserving noise interpolation scheme, allowing gradients to propagate through the discrete selection process. Extensive experiments on LLaVA-v1.5-7B and Qwen2.5-VL-7B demonstrate that our approach consistently outperforms fixed-ratio baselines across different compression levels. Under aggressive pruning that removes 88.9% of visual tokens, our method preserves 94.6% of the original accuracy while achieving a 1.88x speed-up in prefill latency.

CARE: Context-Aware Ranking Evolution with Executable Scoring Programs for Budgeted Reaction Optimization

High-throughput experimentation can evaluate many reaction conditions, yet combinatorial condition spaces still exceed the available experiment budget. This makes experiment selection a sequential decision problem: each new condition must be chosen from limited observations before its outcome is known. LLMs can express task-specific selection logic. A direct recommendation, however, is neither a persistent executable object that can be validated and revised nor an independently auditable decision rule. We introduce CARE, a reference-conditioned controller that separates program synthesis from experiment selection. An LLM writes an executable scoring program that ranks the remaining conditions, while a non-LLM reference policy supplies a numerical candidate and support summary. CARE forms an optional alternative from the program, applies a reference-conditioned intervention gate to compare it with the reference, and records the decision before the selected outcome is revealed. Each new outcome updates controller state and can trigger retention, revision, or regeneration of the active program. This outcome-guided program evolution changes the scoring logic without updating the LLM parameters. In matched offline replay with 30 seeds on eight reaction-optimization tasks, CARE attains the lowest normalized regret, the highest normalized best-so-far AUC, and the highest Top-1% Success@15 among the evaluated methods. These results support using a scoring program written by an LLM as one component of a reference-conditioned optimizer rather than as a standalone experiment selector.

Trading Utility for Dynamic Fairness in Multiple Resource Division with Sequential Demand

Dynamic multi-resource allocation is a central problem in shared computing environments, where users' demands arrive sequentially and resources must be distributed fairly without knowledge of future demands. Existing methods emphasize fairness guarantees such as Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, but often overlook system utility. Moreover, these fairness criteria are mutually incompatible, preventing strict enforcement of them at the same time. We propose a neural allocation mechanism that reconciles fairness with utility through multi-objective optimization during sequential rollout. We first formalize fairness in the dynamic setting via stepwise loss functions for Sharing Incentive, Envy Freeness, and Dynamic Pareto Optimality, enabling differentiable training. Leveraging non-wastefulness, we parameterized the solutions by constraining allocations to the subspace of demand while allowing elastic over-allocation when resources remain available. Empirical results demonstrate that our learned allocator achieves substantially higher utility at comparable levels of fairness, uncovering clear Pareto-frontier-like tradeoffs across metrics.

Mind the Sim-to-Real Gap & Think Like a Scientist

Suppose a planner has a pre-trained simulator of a sequential decision problem and the option to run real experiments in the field. The simulator is cheap to query but inherits confounding and drift from its calibration data. Experimentation is unbiased but consumes one real unit per trial. We study when, and how, the planner should supplement the simulator with experiments. We give three results. First, an extended simulation lemma decomposes the simulator's value error into a calibration--deployment shift that randomization can identify and a parametric residual that no further interaction can reduce. Second, the value gap between the simulator-optimal policy and the optimum splits into a local component, on states the deployed policy already visits, and a reachability component, on states it does not. The reachability component stays bounded away from zero at any horizon under purely passive learning. Third, we propose Fisher-SEP, a simulation-aided experimental policy (SEP) that minimizes the posterior predictive variance of a target policy's value, with reward-only and transition-only specializations. Two case studies illustrate the regimes. In a vending-machine supply chain, front-loaded experimentation overtakes posterior updating once the horizon is long enough to amortize the pilot. In an HIV mobile-testing example with a corridor that separates a well-surveilled region from a poorly-surveilled one, only designed exploration reaches the poorly-surveilled region.

KellyBench: A Benchmark for Long-Horizon Sequential Decision Making

Language models are saturating benchmarks for procedural tasks with narrow objectives. But they are increasingly being deployed in long-horizon, non-stationary environments with open-ended goals. In this paper we introduce KellyBench, an environment for evaluating sequential decision-making in sports betting markets. Agents are placed in a sequential simulation of the 2023-24 English Premier League season and tasked with maximising their long-term bankroll growth. They are given detailed historical data, including advanced statistics, lineups, and public odds. To succeed they must build machine learning models, identify edge in public markets, and adapt as the environment changes over time. We find that all frontier models evaluated lose money on average over the course of the season for five seeds. The best performing model achieves an average return of -8%, and many models experiencing ruin across seeds. To judge strategy sophistication, we use a human expert rubric to grade each model and find their approaches to be unsophisticated compared to human baselines; Claude Opus 4.6 achieves a rubric score of 26.5%, which means there is significant room for improvement. KellyBench is available as an open-access API endpoint at https://openreward.ai/GeneralReasoning/KellyBench.