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In this paper, we study the Temporal Difference (TD) learning with linear value function approximation. It is well known that most TD learning algorithms are unstable with linear function approximation and off-policy learning. Recent…

The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational…

In this paper, based on the Tikhonov regularization technique, we study a monotone general variational inequality (GVI) by considering an associated strongly monotone GVI, depending on a regularization parameter $\alpha,$ such that the…

Reinforcement Learning with Verifiable Rewards (RLVR), which uses simple binary feedback to post-train large language models, has found significant empirical success. However, a principled understanding of why it works is lacking. This…

The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that…

Reinforcement learning (RL) has shown empirical success in various real world settings with complex models and large state-action spaces. The existing analytical results, however, typically focus on settings with a small number of…

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a critical method for enhancing the reasoning capabilities of Large Language Models (LLMs). However, continuous training often leads to policy entropy collapse,…

Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of…

Reinforcement learning with verifiable rewards (RLVR) has become a standard paradigm for post-training language models, but in practice, verifiers are rarely perfect. Recent theoretical work predicts that verifier noise affects the rate of…

Graph continual learning (GCL) aims to learn from a continuous sequence of graph-based tasks. Regularization methods are vital for preventing catastrophic forgetting in GCL, particularly in the challenging replay-free, class-incremental…

Alignment is vital for safely deploying large language models (LLMs). Existing techniques are either reward-based (training a reward model on preference pairs and optimizing with reinforcement learning) or reward-free (directly fine-tuning…

Temporal difference (TD) learning is a foundational algorithm in reinforcement learning (RL). For nearly forty years, TD learning has served as a workhorse for applied RL as well as a building block for more complex and specialized…

Studies on generalization performance of machine learning algorithms under the scope of information theory suggest that compressed representations can guarantee good generalization, inspiring many compression-based regularization methods.…

We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of…

We study risk-sensitive reinforcement learning (RL) based on an entropic risk measure in episodic non-stationary Markov decision processes (MDPs). Both the reward functions and the state transition kernels are unknown and allowed to vary…

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as an important paradigm for unlocking reasoning capabilities in large language models, exemplified by the success of OpenAI o1 and DeepSeek-R1. Currently, Group Relative…

We introduce a novel method that averages the logits of a frozen reference policy (e.g., SFT) and a trainable policy, and incorporate the method into Group Relative Policy Optimization (GRPO). In contrast to Reinforcement Learning with…

Reinforcement Learning with Verifiable Rewards (RLVR) is a key paradigm for improving large-scale reasoning models. Unlike supervised fine-tuning (SFT), RLVR exhibits distinct optimization dynamics and is sensitive to the preservation of…

Reinforcement Learning with Verifiable Rewards (RLVR) has become an effective post-training method for improving the reasoning abilities of Large Language Models (LLMs). However, existing methods mainly apply uniform optimization…

Reinforcement Learning with Verifiable Rewards (RLVR) serves as a cornerstone technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, its training is often plagued by \emph{entropy collapse}, a rapid…