Learning the Supports for Categorical Critic in Reinforcement Learning

Start Classifying: Categorical Critics for LLM Reinforcement Learning

Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.

Simple Actors and Deep Critics for Scalable Reinforcement Learning

Recent progress in offline reinforcement learning (RL) has been driven by expressive generative actors such as diffusion and flow-matching policies, which capture multimodal behavior in offline datasets. However, these actors require multiple denoising or integration steps per action and thus incur substantial overhead at every decision in deployment. In this work, we revisit where capacity should be invested in an offline actor--critic method. Since the critic is used only during training and is discarded at deployment while the actor runs at every decision step, allocating capacity to the critic rather than the actor is more favorable for inference-time efficiency. However, scaling MLP critics in offline RL is known to introduce several distinct instabilities that have, in practice, kept critics shallow. We identify three distinct failure modes that arise when critics are deepened in offline RL---optimization, bootstrap-noise amplification, and value-range drift---and address each with a corresponding ingredient: a residual MLP backbone, n-step bootstrap targets, and a categorical cross-entropy loss. Combining these ingredients with a lightweight deterministic actor, we propose LAC (Light Actor, deep Critic). On OGBench, LAC matches the strongest diffusion- and flow-matching baselines while achieving up to 4x lower inference latency, comparable to one-step distilled policies without distillation. Its critic recipe also transfers across actor parametrizations.

Reducing Scalar Rewards to Binary Success: General Off-Policy Learning with Success Functions

LEMUR: Learning to Align with Multi-Objective Reinforcement Learning from Preference Feedback

Reinforcement Learning (RL) systems are typically trained using a single, well-specified scalar reward function. However, real-world decision-making tasks often involve multiple, competing objectives, such as performance versus efficiency, where ground-truth reward functions are difficult to specify or inaccessible. While Multi-Objective RL (MORL) addresses such trade-offs by modeling rewards as vectors, existing approaches typically assume access to a well-specified reward function for each objective, inheriting the same challenges faced by single-objective RL. Meanwhile, Preference-based RL (PbRL) has shown great potential in solving complex tasks without access to a pre-defined reward function through reward learning from human feedback, yet has largely been studied in single-objective settings. In this work, we bridge this gap with LEMUR: Learning to Align with Multi-Objective Reinforcement Learning with Preference feedback, a novel framework where an agent interactively learns from the preferences of multiple humans to learn optimal multi-objective policies. Our approach jointly learns policies and multiple objective-specific reward models from human feedback, enabling agents to effectively balance competing objectives during learning. We evaluate LEMUR on a variety of benchmark multi-objective tasks, and empirical results demonstrate its superior performance over baseline methods. Our method presents a promising direction for solving multi-objective decision-making tasks without pre-defined reward functions.

Efficient Hypergradient Descent for Inverse Reinforcement Learning

Inverse reinforcement learning (IRL) aims to recover a reward function under which the resulting policy reproduces the behavior observed in expert demonstrations. A natural approach is to formulate IRL as a bilevel optimization problem, in which the inner level corresponds to policy optimization under the learned reward and the outer level measures the discrepancy between the induced policy and expert data. However, this formulation is computationally challenging in practice because the outer update requires a hypergradient involving an inverse-Hessian-vector product for the inner objective. We address this challenge by showing that, at the inner optimum, the Hessian of the inner objective is proportional to the Fisher information matrix of the policy, yielding a structured Fisher-based hypergradient closely related to Natural Hypergradient Descent. To address the resulting scalability bottleneck associated with large Fisher matrices, we approximate the required inverse-Fisher-vector product using a streaming spectral sketch, avoiding explicit construction of the Fisher matrix. We evaluate our approach against a first-order stochastic bilevel baseline across discrete- and continuous-control environments. The results demonstrate competitive policy performance and strong reward-ranking quality, while Fisher sketching reduces curvature-storage complexity and can improve computational efficiency relative to an explicit Fisher solver.

Constrained Reinforcement Learning Using Successor Representations

Real-world Reinforcement Learning depends on the ability to formulate safety constraints into a policy. A common way to model such constraints is to introduce an additional cost signal in the Markov Decision Process, which notifies the agent of unwanted behavior independently of the reward signal. Unfortunately, current methods are hard to adapt to changes in the cost function introduced by, e.g., domain shift or obstacles moving over time. The lack of adaptability means that policies are too unflexible to deal with complex real-world conditions. We propose the Safe Deep Successor Representation (SafeDSR), a novel method that allows quick retraining of policies towards new cost structures. SafeDSR extends the Deep Successor Representation (Kulkarni et al., 2016) to Constrained Reinforcement Learning by introducing a single learnable weight matrix to decouple the learned value function across dynamics, rewards, and costs. This matrix can be updated in a supervised manner instead of having to adapt the whole network if the cost structure of the environment changes. We demonstrate this ability in a freely configurable two-dimensional navigation environment and show that our method is competitive on a simple navigation task while being considerably more flexible