Equivalence of stochastic and deterministic policy gradients

Policy gradients in continuous control have been derived for both stochastic and deterministic policies. Here we study the relationship between the two. In a widely-used family of MDPs involving Gaussian control noise and quadratic control costs, we show that the stochastic and deterministic policy gradients, natural gradients, and state value functions are identical; while the state-control value functions are different. We then develop a general procedure for constructing an MDP with deterministic policy that is equivalent to a given MDP with stochastic policy. The controls of this new MDP are the sufficient statistics of the stochastic policy in the original MDP. Our results suggest that policy gradient methods can be unified by approximating state value functions rather than state-control value functions.

On Global Convergence Rates for Federated Policy Gradient under Heterogeneous Environment

Ensuring convergence of policy gradient methods in federated reinforcement learning (FRL) under environment heterogeneity remains a major challenge. In this work, we first establish that heterogeneity, perhaps counter-intuitively, can necessitate optimal policies to be non-deterministic or even time-varying, even in tabular environments. Subsequently, we prove global convergence results for federated policy gradient (FedPG) algorithms employing local updates, under a {\L}ojasiewicz condition that holds only for each individual agent, in both entropy-regularized and non-regularized scenarios. Crucially, our theoretical analysis shows that FedPG attains linear speed-up with respect to the number of agents, a property central to efficient federated learning. Leveraging insights from our theoretical findings, we introduce b-RS-FedPG, a novel policy gradient method that employs a carefully constructed softmax-inspired parameterization coupled with an appropriate regularization scheme. We further demonstrate explicit convergence rates for b-RS-FedPG toward near-optimal stationary policies. Finally, we demonstrate that empirically both FedPG and b-RS-FedPG consistently outperform federated Q-learning on heterogeneous settings.

Enhanced DACER Algorithm with High Diffusion Efficiency

Due to their expressive capacity, diffusion models have shown great promise in offline RL and imitation learning. Diffusion Actor-Critic with Entropy Regulator (DACER) extended this capability to online RL by using the reverse diffusion process as a policy approximator, trained end-to-end with policy gradient methods, achieving strong performance. However, this comes at the cost of requiring many diffusion steps, which significantly hampers training efficiency, while directly reducing the steps leads to noticeable performance degradation. Critically, the lack of inference efficiency becomes a significant bottleneck for applying diffusion policies in real-time online RL settings. To improve training and inference efficiency while maintaining or even enhancing performance, we propose a Q-gradient field objective as an auxiliary optimization target to guide the denoising process at each diffusion step. Nonetheless, we observe that the independence of the Q-gradient field from the diffusion time step negatively impacts the performance of the diffusion policy. To address this, we introduce a temporal weighting mechanism that enables the model to efficiently eliminate large-scale noise in the early stages and refine actions in the later stages. Experimental results on MuJoCo benchmarks and several multimodal tasks demonstrate that the DACER2 algorithm achieves state-of-the-art performance in most MuJoCo control tasks with only five diffusion steps, while also exhibiting stronger multimodality compared to DACER.

The challenge of hidden gifts in multi-agent reinforcement learning

Sometimes we benefit from actions that others have taken even when we are unaware that they took those actions. For example, if your neighbor chooses not to take a parking spot in front of your house when you are not there, you can benefit, even without being aware that they took this action. These "hidden gifts" represent an interesting challenge for multi-agent reinforcement learning (MARL), since assigning credit when the beneficial actions of others are hidden is non-trivial. Here, we study the impact of hidden gifts with a very simple MARL task. In this task, agents in a grid-world environment have individual doors to unlock in order to obtain individual rewards. As well, if all the agents unlock their door the group receives a larger collective reward. However, there is only one key for all of the doors, such that the collective reward can only be obtained when the agents drop the key for others after they use it. Notably, there is nothing to indicate to an agent that the other agents have dropped the key, thus the act of dropping the key for others is a "hidden gift". We show that several different state-of-the-art RL algorithms, including MARL algorithms, fail to learn how to obtain the collective reward in this simple task. Interestingly, we find that independent model-free policy gradient agents can solve the task when we provide them with information about their own action history, but MARL agents still cannot solve the task with action history. Finally, we derive a correction term for these independent agents, inspired by learning aware approaches, which reduces the variance in learning and helps them to converge to collective success more reliably. These results show that credit assignment in multi-agent settings can be particularly challenging in the presence of "hidden gifts", and demonstrate that learning awareness in independent agents can benefit these settings.

On-Policy RL with Optimal Reward Baseline

Reinforcement learning algorithms are fundamental to align large language models with human preferences and to enhance their reasoning capabilities. However, current reinforcement learning algorithms often suffer from training instability due to loose on-policy constraints and computational inefficiency due to auxiliary models. In this work, we propose On-Policy RL with Optimal reward baseline (OPO), a novel and simplified reinforcement learning algorithm designed to address these challenges. OPO emphasizes the importance of exact on-policy training, which empirically stabilizes the training process and enhances exploration. Moreover, OPO introduces the optimal reward baseline that theoretically minimizes gradient variance. We evaluate OPO on mathematical reasoning benchmarks. The results demonstrate its superior performance and training stability without additional models or regularization terms. Furthermore, OPO achieves lower policy shifts and higher output entropy, encouraging more diverse and less repetitive responses. These results highlight OPO as a promising direction for stable and effective reinforcement learning in large language model alignment and reasoning tasks. The implementation is provided at https://github.com/microsoft/LMOps/tree/main/opo.

Bigger, Regularized, Categorical: High-Capacity Value Functions are Efficient Multi-Task Learners

Recent advances in language modeling and vision stem from training large models on diverse, multi-task data. This paradigm has had limited impact in value-based reinforcement learning (RL), where improvements are often driven by small models trained in a single-task context. This is because in multi-task RL sparse rewards and gradient conflicts make optimization of temporal difference brittle. Practical workflows for generalist policies therefore avoid online training, instead cloning expert trajectories or distilling collections of single-task policies into one agent. In this work, we show that the use of high-capacity value models trained via cross-entropy and conditioned on learnable task embeddings addresses the problem of task interference in online RL, allowing for robust and scalable multi-task training. We test our approach on 7 multi-task benchmarks with over 280 unique tasks, spanning high degree-of-freedom humanoid control and discrete vision-based RL. We find that, despite its simplicity, the proposed approach leads to state-of-the-art single and multi-task performance, as well as sample-efficient transfer to new tasks.

Frequency Resource Management in 6G User-Centric CFmMIMO: A Hybrid Reinforcement Learning and Metaheuristic Approach

As sixth-generation (6G) networks continue to evolve, AI-driven solutions are playing a crucial role in enabling more efficient and adaptive resource management in wireless communication. One of the key innovations in 6G is user-centric cell-free massive Multiple-Input Multiple-Output (UC-CFmMIMO), a paradigm that eliminates traditional cell boundaries and enhances network performance by dynamically assigning access points (APs) to users. This approach is particularly well-suited for vehicular networks, offering seamless, homogeneous, ultra-reliable, and low-latency connectivity. However, in dense networks, a key challenge lies in efficiently allocating frequency resources within a limited shared subband spectrum while accounting for frequency selectivity and the dependency of signal propagation on bandwidth. These factors make resource allocation increasingly complex, especially in dynamic environments where maintaining Quality of Service (QoS) is critical. This paper tackles these challenges by proposing a hybrid multi-user allocation strategy that integrates reinforcement learning (RL) and metaheuristic optimization to enhance spectral efficiency (SE), ensure fairness, and mitigate interference within shared subbands. To assess its effectiveness, we compare this hybrid approach with two other methods: the bio-inspired Aquila Optimizer (AO) and Deep Deterministic Policy Gradient (DDPG)-based Actor-Critic Reinforcement Learning (AC-RL). Our evaluation is grounded in real-world patterns and channel characteristics, utilizing the 3GPP-3D channel modeling framework (QuaDRiGa) to capture realistic propagation conditions. The results demonstrate that the proposed hybrid strategy achieves a superior balance among competing objectives, underscoring the role of AI-driven resource allocation in advancing UC-CFmMIMO systems for next-generation wireless networks.

The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models

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.

Text2Grad: Reinforcement Learning from Natural Language Feedback

Traditional RLHF optimizes language models with coarse, scalar rewards that mask the fine-grained reasons behind success or failure, leading to slow and opaque learning. Recent work augments RL with textual critiques through prompting or reflection, improving interpretability but leaving model parameters untouched. We introduce Text2Grad, a reinforcement-learning paradigm that turns free-form textual feedback into span-level gradients. Given human (or programmatic) critiques, Text2Grad aligns each feedback phrase with the relevant token spans, converts these alignments into differentiable reward signals, and performs gradient updates that directly refine the offending portions of the model's policy. This yields precise, feedback-conditioned adjustments instead of global nudges. Text2Grad is realized through three components: (1) a high-quality feedback-annotation pipeline that pairs critiques with token spans; (2) a fine-grained reward model that predicts span-level reward on answer while generating explanatory critiques; and (3) a span-level policy optimizer that back-propagates natural-language gradients. Across summarization, code generation, and question answering, Text2Grad consistently surpasses scalar-reward RL and prompt-only baselines, providing both higher task metrics and richer interpretability. Our results demonstrate that natural-language feedback, when converted to gradients, is a powerful signal for fine-grained policy optimization. The code for our method is available at https://github.com/microsoft/Text2Grad

SDPO: Importance-Sampled Direct Preference Optimization for Stable Diffusion Training

Preference learning has become a central technique for aligning generative models with human expectations. Recently, it has been extended to diffusion models through methods like Direct Preference Optimization (DPO). However, existing approaches such as Diffusion-DPO suffer from two key challenges: timestep-dependent instability, caused by a mismatch between the reverse and forward diffusion processes and by high gradient variance in early noisy timesteps, and off-policy bias arising from the mismatch between optimization and data collection policies. We begin by analyzing the reverse diffusion trajectory and observe that instability primarily occurs at early timesteps with low importance weights. To address these issues, we first propose DPO-C\&M, a practical strategy that improves stability by clipping and masking uninformative timesteps while partially mitigating off-policy bias. Building on this, we introduce SDPO (Importance-Sampled Direct Preference Optimization), a principled framework that incorporates importance sampling into the objective to fully correct for off-policy bias and emphasize informative updates during the diffusion process. Experiments on CogVideoX-2B, CogVideoX-5B, and Wan2.1-1.3B demonstrate that both methods outperform standard Diffusion-DPO, with SDPO achieving superior VBench scores, human preference alignment, and training robustness. These results highlight the importance of timestep-aware, distribution-corrected optimization in diffusion-based preference learning.