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We propose Orthogonalized Policy Optimization (OPO), a principled framework for large language model alignment derived from optimization in the Hilbert function space L2(pi_k). Lifting policy updates from the probability simplex into…

机器学习 · 计算机科学 2026-02-26 Wang Zixian

Reinforcement Learning with Verifiable Rewards (RLVR) has become a promising paradigm for scaling reasoning capabilities of Large Language Models (LLMs). However, the sparsity of binary verifier rewards often leads to low efficiency and…

机器学习 · 计算机科学 2026-05-22 Shuo Yang , Jinda Lu , Kexin Huang , Chiyu Ma , Shaohang Wei , Yuyang Liu , Guoyin Wang , Jingren Zhou , Li Yuan

Traditional policy gradient methods are fundamentally flawed. Natural gradients converge quicker and better, forming the foundation of contemporary Reinforcement Learning such as Trust Region Policy Optimization (TRPO) and Proximal Policy…

机器学习 · 计算机科学 2022-09-07 W. J. A. van Heeswijk

We consider the problem of learning control policies that optimize a reward function while satisfying constraints due to considerations of safety, fairness, or other costs. We propose a new algorithm, Projection-Based Constrained Policy…

机器学习 · 计算机科学 2020-10-08 Tsung-Yen Yang , Justinian Rosca , Karthik Narasimhan , Peter J. Ramadge

Proximal constraints are fundamental to the stability of the Large Language Model reinforcement learning. While the canonical clipping mechanism in PPO serves as an efficient surrogate for trust regions, we identify a critical bottleneck:…

机器学习 · 计算机科学 2026-03-06 Yuan Li , Bo Wang , Yufei Gao , Yuqian Yao , Xinyuan Wang , Zhangyue Yin , Xipeng Qiu

Wasserstein distributionally robust optimization (WDRO) strengthens statistical learning under model uncertainty by minimizing the local worst-case risk within a prescribed ambiguity set. Although WDRO has been extensively studied in…

机器学习 · 统计学 2025-11-12 Changyu Liu , Yuling Jiao , Junhui Wang , Jian Huang

Sampling-based model predictive control (MPC) algorithms, such as model predictive path integral (MPPI), enable approximate, gradient-free solutions to optimal control problems by drawing samples from a proposal distribution, evaluating…

系统与控制 · 电气工程与系统科学 2026-05-11 Markus Walker , Marcel Reith-Braun , Daniel Frisch , Uwe D. Hanebeck

Many of the recent trajectory optimization algorithms alternate between linear approximation of the system dynamics around the mean trajectory and conservative policy update. One way of constraining the policy change is by bounding the…

机器学习 · 计算机科学 2018-07-03 Riad Akrour , Abbas Abdolmaleki , Hany Abdulsamad , Jan Peters , Gerhard Neumann

In recent years, trust region on-policy reinforcement learning has achieved impressive results in addressing complex control tasks and gaming scenarios. However, contemporary state-of-the-art algorithms within this category primarily…

机器学习 · 计算机科学 2024-05-31 Weiye Zhao , Feihan Li , Yifan Sun , Rui Chen , Tianhao Wei , Changliu Liu

Wasserstein distributionally robust optimization (WDRO) attempts to learn a model that minimizes the local worst-case risk in the vicinity of the empirical data distribution defined by Wasserstein ball. While WDRO has received attention as…

机器学习 · 统计学 2020-06-23 Yongchan Kwon , Wonyoung Kim , Joong-Ho Won , Myunghee Cho Paik

In order for reinforcement learning techniques to be useful in real-world decision making processes, they must be able to produce robust performance from limited data. Deep policy optimization methods have achieved impressive results on…

机器学习 · 计算机科学 2020-12-22 James Queeney , Ioannis Ch. Paschalidis , Christos G. Cassandras

We propose a new family of policy gradient methods for reinforcement learning, which alternate between sampling data through interaction with the environment, and optimizing a "surrogate" objective function using stochastic gradient ascent.…

机器学习 · 计算机科学 2017-08-29 John Schulman , Filip Wolski , Prafulla Dhariwal , Alec Radford , Oleg Klimov

We present Group Orthogonalized Policy Optimization (GOPO), a new alignment algorithm for large language models derived from the geometry of Hilbert function spaces. Instead of optimizing on the probability simplex and inheriting the…

机器学习 · 计算机科学 2026-02-26 Wang Zixian

We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…

最优化与控制 · 数学 2025-03-27 Jie Wang , Rui Gao , Yao Xie

Most of reinforcement learning algorithms optimize the discounted criterion which is beneficial to accelerate the convergence and reduce the variance of estimates. Although the discounted criterion is appropriate for certain tasks such as…

机器学习 · 计算机科学 2021-11-02 Xiaoteng Ma , Xiaohang Tang , Li Xia , Jun Yang , Qianchuan Zhao

Natural policy gradient (NPG) methods are among the most widely used policy optimization algorithms in contemporary reinforcement learning. This class of methods is often applied in conjunction with entropy regularization -- an algorithmic…

机器学习 · 统计学 2022-09-13 Shicong Cen , Chen Cheng , Yuxin Chen , Yuting Wei , Yuejie Chi

This paper is devoted to the stochastic approximation of entropically regularized Wasserstein distances between two probability measures, also known as Sinkhorn divergences. The semi-dual formulation of such regularized optimal…

统计理论 · 数学 2024-12-10 Bernard Bercu , Jérémie Bigot

Reinforcement Learning (RL) agents can solve diverse tasks but often exhibit unsafe behavior. Constrained Markov Decision Processes (CMDPs) address this by enforcing safety constraints, yet existing methods either sacrifice reward…

机器学习 · 计算机科学 2025-08-18 Nikola Milosevic , Johannes Müller , Nico Scherf

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training large language models. While Group Relative Policy Optimization (GRPO) is widely adopted, its coarse credit assignment uniformly…

机器学习 · 计算机科学 2026-04-03 Gengsheng Li , Tianyu Yang , Junfeng Fang , Mingyang Song , Mao Zheng , Haiyun Guo , Dan Zhang , Jinqiao Wang , Tat-Seng Chua

While Group Relative Policy Optimization (GRPO) has emerged as a scalable framework for critic-free policy learning, extending it to settings with explicit behavioral constraints remains underexplored. We introduce Constrained GRPO, a…

机器学习 · 计算机科学 2026-02-09 Roger Girgis , Rodrigue de Schaetzen , Luke Rowe , Azalée Robitaille , Christopher Pal , Liam Paull