Recent advances in aligning large language models with human preferences have corroborated the growing importance of best-of-$N$ distillation (BOND). However, the iterative BOND algorithm is prohibitively expensive in practice due to the sample and computation inefficiency. This paper addresses the problem by revealing a unified game-theoretic connection between iterative BOND and self-play alignment, which unifies seemingly disparate algorithmic paradigms. Based on the connection, we establish a novel framework, \textbf{WIN} rate \textbf{D}ominance (WIND), with a series of efficient algorithms for regularized win rate dominance optimization that approximates iterative BOND in the parameter space. We provides provable sample efficiency guarantee for one of the WIND variant with the square loss objective. The experimental results confirm that our algorithm not only accelerates the computation, but also achieves superior sample efficiency compared to existing methods.

Reinforcement learning from human feedback (RLHF) has demonstrated great promise in aligning large language models (LLMs) with human preference. Depending on the availability of preference data, both online and offline RLHF are active areas of investigation. A key bottleneck is understanding how to incorporate uncertainty estimation in the reward function learned from the preference data for RLHF, regardless of how the preference data is collected. While the principles of optimism or pessimism under uncertainty are well-established in standard reinforcement learning (RL), a practically-implementable and theoretically-grounded form amenable to large language models is not yet available, as standard techniques for constructing confidence intervals become intractable under arbitrary policy parameterizations. In this paper, we introduce a unified approach to online and offline RLHF --- value-incentivized preference optimization (VPO) --- which regularizes the maximum-likelihood estimate of the reward function with the corresponding value function, modulated by a sign to indicate whether the optimism or pessimism is chosen. VPO also directly optimizes the policy with implicit reward modeling, and therefore shares a simpler RLHF pipeline similar to direct preference optimization. Theoretical guarantees of VPO are provided for both online and offline settings, matching the rates of their standard RL counterparts. Moreover, experiments on text summarization, dialogue, and standard benchmarks verify the practicality and effectiveness of VPO.

Federated reinforcement learning (RL) enables collaborative decision making of multiple distributed agents without sharing local data trajectories. In this work, we consider a multi-task setting, in which each agent has its own private reward function corresponding to different tasks, while sharing the same transition kernel of the environment. Focusing on infinite-horizon Markov decision processes, the goal is to learn a globally optimal policy that maximizes the sum of the discounted total rewards of all the agents in a decentralized manner, where each agent only communicates with its neighbors over some prescribed graph topology. We develop federated vanilla and entropy-regularized natural policy gradient (NPG) methods in the tabular setting under softmax parameterization, where gradient tracking is applied to estimate the global Q-function to mitigate the impact of imperfect information sharing. We establish non-asymptotic global convergence guarantees under exact policy evaluation, where the rates are nearly independent of the size of the state-action space and illuminate the impacts of network size and connectivity. To the best of our knowledge, this is the first time that global convergence is established for federated multi-task RL using policy optimization. We further go beyond the tabular setting by proposing a federated natural actor critic (NAC) method for multi-task RL with function approximation, and establish its finite-time sample complexity taking the errors of function approximation into account.

This paper investigates the problem of computing the equilibrium of competitive games in the form of two-player zero-sum games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding the last-iterate convergence of extragradient methods in the unconstrained setting, the theoretical underpinnings of these methods in the constrained settings, especially those using multiplicative updates, remain highly inadequate, even when the objective function is bilinear. Motivated by the algorithmic role of entropy regularization in single-agent reinforcement learning and game theory, we develop provably efficient extragradient methods to find the quantal response equilibrium (QRE)---which are solutions to zero-sum two-player matrix games with entropy regularization---at a linear rate. The proposed algorithms can be implemented in a decentralized manner, where each player executes symmetric and multiplicative updates iteratively using its own payoff without observing the opponent's actions directly. In addition, by controlling the knob of entropy regularization, the proposed algorithms can locate an approximate Nash equilibrium of the unregularized matrix game at a sublinear rate without assuming the Nash equilibrium to be unique. Our methods also lead to efficient policy extragradient algorithms for solving (entropy-regularized) zero-sum Markov games at similar rates. All of our convergence rates are nearly dimension-free, which are independent of the size of the state and action spaces up to logarithm factors, highlighting the positive role of entropy regularization for accelerating convergence.

This paper investigates the problem of computing the equilibrium of competitive games, which is often modeled as a constrained saddle-point optimization problem with probability simplex constraints. Despite recent efforts in understanding the last-iterate convergence of extragradient methods in the unconstrained setting, the theoretical underpinnings of these methods in the constrained settings, especially those using multiplicative updates, remain highly inadequate, even when the objective function is bilinear. Motivated by the algorithmic role of entropy regularization in single-agent reinforcement learning and game theory, we develop provably efficient extragradient methods to find the quantal response equilibrium (QRE)---which are solutions to zero-sum two-player matrix games with entropy regularization---at a linear rate. The proposed algorithms can be implemented in a decentralized manner, where each player executes symmetric and multiplicative updates iteratively using its own payoff without observing the opponent's actions directly. In addition, by controlling the knob of entropy regularization, the proposed algorithms can locate an approximate Nash equilibrium of the unregularized matrix game at a sublinear rate without assuming the Nash equilibrium to be unique. Our methods also lead to efficient policy extragradient algorithms for solving entropy-regularized zero-sum Markov games at a linear rate. All of our convergence rates are nearly dimension-free, which are independent of the size of the state and action spaces up to logarithm factors, highlighting the positive role of entropy regularization for accelerating convergence.

Due to the imminent need to alleviate the communication burden in multi-agent and federated learning, the investigation of communication-efficient distributed optimization algorithms for empirical risk minimization has flourished recently. A large fraction of existing algorithms are developed for the master/slave setting, relying on the presence of a central parameter server. This paper focuses on distributed optimization in the network setting (also known as the decentralized setting), where each agent is only allowed to aggregate information from its neighbors over a graph. By properly adjusting the global gradient estimate via a tracking term, we first develop a communication-efficient approximate Newton-type method, called Network-DANE, which generalizes the attractive DANE algorithm to decentralized networks. Our key algorithmic ideas can be applied, in a systematic manner, to obtain decentralized versions of other master/slave distributed algorithms. Notably, we develop Network-SVRG/SARAH, which employ stochastic variance reduction at each agent to accelerate local computations. We establish linear convergence of Network-DANE and Network-SVRG for strongly convex losses, and Network-SARAH for quadratic losses, which shed light on the impact of data homogeneity, network connectivity, and local averaging upon the rate of convergence. Numerical evidence is provided to demonstrate the appealing performance of our algorithms over competitive baselines, in terms of both communication and computation efficiency.

There is growing interest in large-scale machine learning and optimization over decentralized networks, e.g. in the context of multi-agent learning and federated learning. Due to the imminent need to alleviate the communication burden, the investigation of communication-efficient distributed optimization algorithms --- particularly for empirical risk minimization --- has flourished in recent years. A large fraction of these algorithms have been developed for the master/slave setting, relying on the presence of a central parameter server that can communicate with all agents. This paper focuses on distributed optimization over networks, or decentralized optimization, where each agent is only allowed to aggregate information from its neighbors over a network (namely, no centralized coordination is present). By properly adjusting the global gradient estimate via local averaging in conjunction with proper correction, we develop a communication-efficient approximate Newton-type method, called Network-DANE, which generalizes DANE to accommodate decentralized scenarios. Our key ideas can be applied, in a systematic manner, to obtain decentralized versions of other master/slave distributed algorithms. A notable development is Network-SVRG/SARAH, which employs variance reduction at each agent to further accelerate local computation. We establish linear convergence of Network-DANE and Network-SVRG for strongly convex losses, and Network-SARAH for quadratic losses, which shed light on the impacts of data homogeneity, network connectivity, and local averaging upon the rate of convergence. We further extend Network-DANE to composite optimization by allowing a nonsmooth penalty term. Numerical evidence is provided to demonstrate the appealing performance of our algorithms over competitive baselines, in terms of both communication and computation efficiency. Our work suggests that by performing a judiciously chosen amount of local communication and computation per iteration, the overall efficiency can be substantially improved.