The relationship between inverse reinforcement learning (IRL) and inverse optimization (IO) for Markov decision processes (MDPs) has been relatively underexplored in the literature, despite addressing the same problem. In this work, we revisit the relationship between the IO framework for MDPs, IRL, and apprenticeship learning (AL). We incorporate prior beliefs on the structure of the cost function into the IRL and AL problems, and demonstrate that the convex-analytic view of the AL formalism (Kamoutsi et al., 2021) emerges as a relaxation of our framework. Notably, the AL formalism is a special case in our framework when the regularization term is absent. Focusing on the suboptimal expert setting, we formulate the AL problem as a regularized min-max problem. The regularizer plays a key role in addressing the ill-posedness of IRL by guiding the search for plausible cost functions. To solve the resulting regularized-convex-concave-min-max problem, we use stochastic mirror descent (SMD) and establish convergence bounds for the proposed method. Numerical experiments highlight the critical role of regularization in learning cost vectors and apprentice policies.

Traditional methods of surgical decision making heavily rely on human experience and prompt actions, which are variable. A data-driven system generating treatment recommendations based on patient states can be a substantial asset in perioperative decision-making, as in cases of intraoperative hypotension, for which suboptimal management is associated with acute kidney injury (AKI), a common and morbid postoperative complication. We developed a Reinforcement Learning (RL) model to recommend optimum dose of intravenous (IV) fluid and vasopressors during surgery to avoid intraoperative hypotension and postoperative AKI. We retrospectively analyzed 50,021 surgeries from 42,547 adult patients who underwent major surgery at a quaternary care hospital between June 2014 and September 2020. Of these, 34,186 surgeries were used for model training and 15,835 surgeries were reserved for testing. We developed a Deep Q-Networks based RL model using 16 variables including intraoperative physiologic time series, total dose of IV fluid and vasopressors extracted for every 15-minute epoch. The model replicated 69% of physician's decisions for the dosage of vasopressors and proposed higher or lower dosage of vasopressors than received in 10% and 21% of the treatments, respectively. In terms of IV fluids, the model's recommendations were within 0.05 ml/kg/15 min of the actual dose in 41% of the cases, with higher or lower doses recommended for 27% and 32% of the treatments, respectively. The model resulted in a higher estimated policy value compared to the physicians' actual treatments, as well as random and zero-drug policies. AKI prevalence was the lowest in patients receiving medication dosages that aligned with model's decisions. Our findings suggest that implementation of the model's policy has the potential to reduce postoperative AKI and improve other outcomes driven by intraoperative hypotension.

This paper aims to overcome a major obstacle in scaling RL for reasoning with LLMs, namely the collapse of policy entropy. Such phenomenon is consistently observed across vast RL runs without entropy intervention, where the policy entropy dropped sharply at the early training stage, this diminished exploratory ability is always accompanied with the saturation of policy performance. In practice, we establish a transformation equation R=-a*e^H+b between entropy H and downstream performance R. This empirical law strongly indicates that, the policy performance is traded from policy entropy, thus bottlenecked by its exhaustion, and the ceiling is fully predictable H=0, R=-a+b. Our finding necessitates entropy management for continuous exploration toward scaling compute for RL. To this end, we investigate entropy dynamics both theoretically and empirically. Our derivation highlights that, the change in policy entropy is driven by the covariance between action probability and the change in logits, which is proportional to its advantage when using Policy Gradient-like algorithms. Empirical study shows that, the values of covariance term and entropy differences matched exactly, supporting the theoretical conclusion. Moreover, the covariance term stays mostly positive throughout training, further explaining why policy entropy would decrease monotonically. Through understanding the mechanism behind entropy dynamics, we motivate to control entropy by restricting the update of high-covariance tokens. Specifically, we propose two simple yet effective techniques, namely Clip-Cov and KL-Cov, which clip and apply KL penalty to tokens with high covariances respectively. Experiments show that these methods encourage exploration, thus helping policy escape entropy collapse and achieve better downstream performance.

Reinforcement Learning (RL) has played a central role in the recent surge of LLMs' math abilities by enabling self-improvement through binary verifier signals. In contrast, Supervised Learning (SL) is rarely considered for such verification-driven training, largely due to its heavy reliance on reference answers and inability to reflect on mistakes. In this work, we challenge the prevailing notion that self-improvement is exclusive to RL and propose Negative-aware Fine-Tuning (NFT) -- a supervised approach that enables LLMs to reflect on their failures and improve autonomously with no external teachers. In online training, instead of throwing away self-generated negative answers, NFT constructs an implicit negative policy to model them. This implicit policy is parameterized with the same positive LLM we target to optimize on positive data, enabling direct policy optimization on all LLMs' generations. We conduct experiments on 7B and 32B models in math reasoning tasks. Results consistently show that through the additional leverage of negative feedback, NFT significantly improves over SL baselines like Rejection sampling Fine-Tuning, matching or even surpassing leading RL algorithms like GRPO and DAPO. Furthermore, we demonstrate that NFT and GRPO are actually equivalent in strict-on-policy training, even though they originate from entirely different theoretical foundations. Our experiments and theoretical findings bridge the gap between SL and RL methods in binary-feedback learning systems.

In multi-agent reinforcement learning (MARL), parameter sharing is commonly employed to enhance sample efficiency. However, the popular approach of full parameter sharing often leads to homogeneous policies among agents, potentially limiting the performance benefits that could be derived from policy diversity. To address this critical limitation, we introduce \emph{Kaleidoscope}, a novel adaptive partial parameter sharing scheme that fosters policy heterogeneity while still maintaining high sample efficiency. Specifically, Kaleidoscope maintains one set of common parameters alongside multiple sets of distinct, learnable masks for different agents, dictating the sharing of parameters. It promotes diversity among policy networks by encouraging discrepancy among these masks, without sacrificing the efficiencies of parameter sharing. This design allows Kaleidoscope to dynamically balance high sample efficiency with a broad policy representational capacity, effectively bridging the gap between full parameter sharing and non-parameter sharing across various environments.

Linear TD($λ$) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold in many practical scenarios. This paper instead establishes the first $L^2$ convergence rates for linear TD($λ$) operating under arbitrary features, without making any algorithmic modification or additional assumptions. Our results apply to both the discounted and average-reward settings. To address the potential non-uniqueness of solutions resulting from arbitrary features, we develop a novel stochastic approximation result featuring convergence rates to the solution set instead of a single point.

This paper introduces a comprehensive framework designed to analyze and secure decision-support systems trained with Deep Reinforcement Learning (DRL), prior to deployment, by providing insights into learned behavior patterns and vulnerabilities discovered through simulation. The introduced framework aids in the development of precisely timed and targeted observation perturbations, enabling researchers to assess adversarial attack outcomes within a strategic decision-making context. We validate our framework, visualize agent behavior, and evaluate adversarial outcomes within the context of a custom-built strategic game, CyberStrike. Utilizing the proposed framework, we introduce a method for systematically discovering and ranking the impact of attacks on various observation indices and time-steps, and we conduct experiments to evaluate the transferability of adversarial attacks across agent architectures and DRL training algorithms. The findings underscore the critical need for robust adversarial defense mechanisms to protect decision-making policies in high-stakes environments.

In this paper, we theoretically study the offline alignment of language models with human preference feedback, under both preference label corruption and privacy protections. To this end, we propose Square$χ$PO, a simple one-line change to $χ$PO where the standard log-loss is replaced by a new square loss over probability. Thanks to the inherent properties of this new loss, we have advanced the state-of-the-art of differentially private and robust offline direct alignment. Specifically, for the local model of label privacy, Square$χ$PO is the first algorithm that attains an optimal rate based on single-policy concentrability even with general function approximations. It also gives the first result under the central model of privacy protection over both prompts (responses) and labels. On the robustness side against Huber label corruption, Square$χ$PO is the first alignment method that has a meaningful theoretical guarantee under general function approximations. More importantly, Square$χ$PO can address privacy protection and corruption simultaneously, where an interesting separation is observed, implying that the order of privacy and corruption matters. Furthermore, we show that Square$χ$PO can also be easily extended to handle the scenario of the general preference model with state-of-the-art guarantees under corruption and privacy. Last but not least, all of our theoretical guarantees enjoy a unified analysis, building upon a new result on the generalization error bounds of least-square regression under corruption and privacy constraints, which we believe is of independent interest to the community.

Long-form question answering (LFQA) presents unique challenges for large language models, requiring the synthesis of coherent, paragraph-length answers. While retrieval-augmented generation (RAG) systems have emerged as a promising solution, existing research struggles with key limitations: the scarcity of high-quality training data for long-form generation, the compounding risk of hallucination in extended outputs, and the absence of reliable evaluation metrics for factual completeness. In this paper, we propose RioRAG, a novel reinforcement learning (RL) framework that advances long-form RAG through reinforced informativeness optimization. Our approach introduces two fundamental innovations to address the core challenges. First, we develop an RL training paradigm of reinforced informativeness optimization that directly optimizes informativeness and effectively addresses the slow-thinking deficit in conventional RAG systems, bypassing the need for expensive supervised data. Second, we propose a nugget-centric hierarchical reward modeling approach that enables precise assessment of long-form answers through a three-stage process: extracting the nugget from every source webpage, constructing a nugget claim checklist, and computing rewards based on factual alignment. Extensive experiments on two LFQA benchmarks LongFact and RAGChecker demonstrate the effectiveness of the proposed method. Our codes are available at https://github.com/RUCAIBox/RioRAG.

Large language models (LLMs) have exhibited extraordinary performance in a variety of tasks while it remains challenging for them to solve complex multi-step tasks as agents. In practice, agents sensitive to the outcome of certain key steps which makes them likely to fail the task because of a subtle mistake in the planning trajectory. Recent approaches resort to calibrating the reasoning process through reinforcement learning. They reward or penalize every reasoning step with process supervision, as known as Process Reward Models (PRMs). However, PRMs are difficult and costly to scale up with a large number of next action candidates since they require extensive computations to acquire the training data through the per-step trajectory exploration. To mitigate this issue, we focus on the relative reward trend across successive reasoning steps and propose maintaining an increasing reward in the collected trajectories for process supervision, which we term Reward Rising Optimization (RRO). Specifically, we incrementally augment the process supervision until identifying a step exhibiting positive reward differentials, i.e. rising rewards, relative to its preceding iteration. This method dynamically expands the search space for the next action candidates, efficiently capturing high-quality data. We provide mathematical groundings and empirical results on the WebShop and InterCode-SQL benchmarks, showing that our proposed RRO achieves superior performance while requiring much less exploration cost.