SearcharxivSearch

arXiv subjects

Shisheng Cui

Publications and source records attributed to Shisheng Cui.

14 recordsLinked to original sources

Towards a Theoretical Understanding to the Generalization of RLHF

Reinforcement Learning from Human Feedback (RLHF) and its variants have emerged as the dominant approaches for aligning Large Language Models with human intent. While empirically effective, the theoretical generalization properties of these methods in high-dimensional settings remain to be explored. To this end, we build the generalization theory on RLHF of LLMs under the linear reward model, through the framework of algorithmic stability. In contrast to the existing works built upon the consistency of maximum likelihood estimations on reward model, our analysis is presented under an end-to-end learning framework, which is consistent with practice. Concretely, we prove that under a key \textbf{feature coverage} condition, the empirical optima of policy model have a generalization bound of order $\mathcal{O}(n^{-\frac{1}{2}})$. Moreover, the results can be extrapolated to parameters obtained by gradient-based learning algorithms, i.e., Gradient Ascent (GA) and Stochastic Gradient Ascent (SGA). Thus, we argue that our results provide new theoretical evidence for the empirically observed generalization of LLMs after RLHF.

cs.LG

Distribution-Centric Policy Optimization Dominates Exploration-Exploitation Trade-off

The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are \textbf{sample-centric}: they seek or bonus rare samples, assuming exploration comes from novel trajectories and tokens. These heuristics depend on the "luck" of informative samples, lack principled control of the policy, and often yield limited or inconsistent gains. In this work, we are the first to introduce a \textbf{distribution-centric} perspective for RL, in which exploration is always guided by a "better" target distribution, and reveal that a policy's ability to resist entropy collapse is governed by the distribution itself rather than individual samples. Building on this insight, we propose Distribution-Centric Policy Optimization (DCPO), which reformulates entropy regulation as distribution-level regularization. DCPO achieves controllable entropy fully on-policy without sampling from external distributions, enabling efficient exploration while maintaining training stability. Across multiple models and seven benchmarks, DCPO improves over GRPO by about 20\% on average. Overall, DCPO replaces sample-level heuristics with distribution-level principles, offering a theoretically grounded and flexible framework for controllable exploration and a stronger EE trade-off. The code is available in https://github.com/597358816/DCPO.

cs.LG

Complexity guarantees for risk-neutral generalized Nash equilibrium problems

In this paper, we address \ac{SGNEP} seeking with risk-neutral agents. Our main contribution lies the development of a stochastic variance-reduced gradient (SVRG) technique, modified to contend with general sample spaces, within a stochastic forward-backward-forward splitting scheme for resolving structured monotone inclusion problems. This stochastic scheme is a double-loop method, in which the mini-batch gradient estimator is computed periodically in the outer loop, while only cheap sampling is required in a frequently activated inner loop, thus achieving significant speed-ups when sampling costs cannot be overlooked. The algorithm is fully distributed and it guarantees almost sure convergence under appropriate batch size and strong monotonicity assumptions. Moreover, it exhibits a linear rate with possible biased estimators, which is rather mild and imposed in many simulation-based optimization schemes. Under monotone regimes, the expectation of the gap function of an averaged iterate diminishes at a suitable sublinear rate while the sample-complexity of computing an $ε$-solution is provably $\mathcal{O}(ε^{-3})$. A numerical study on a class of networked Cournot games reflects the performance of our proposed algorithm.

math.OC

Self-tuned Regularized Federated Methods with Guarantees for Optimal Solution Selection

We study a hierarchical federated learning (FL) problem, where clients cooperatively seek to select among multiple optimal solutions of a primary distributed learning problem, a solution that minimizes a secondary loss function. This problem arises from over-parameterized learning and ill-posed optimization problems. First, we consider the setting where the inner-level objective is convex and the outer-level objective is either convex or strongly convex. We propose a self-tuned regularized federated averaging (StR-FedAvg) method where the stepsize and regularization parameter are characterized by the number of communication rounds and problem parameters. We derive new complexity guarantees for addressing the optimal solution selection problem in FL. Second, when the outer-level objective is nonconvex, we propose a two-loop FL scheme in which the outer loop employs an inexact projected first-order method and the inner loop applies StR-FedAvg with an iteratively updated regularization parameter. We derive new communication complexity guarantees for computing a stationary point of the nonconvex solution-selection problem. To our knowledge, this is the first work to establish complexity guarantees for this class of problems in FL. Preliminary experiments validate our theoretical findings.

math.OC

Shuffling Gradient Descent-Ascent with Variance Reduction for Nonconvex-Strongly Concave Smooth Minimax Problems

In recent years, there has been considerable interest in designing stochastic first-order algorithms to tackle finite-sum smooth minimax problems. To obtain the gradient estimates, one typically relies on the uniform sampling-with-replacement scheme or various sampling-without-replacement (also known as shuffling) schemes. While the former is easier to analyze, the latter often have better empirical performance. In this paper, we propose a novel single-loop stochastic gradient descent-ascent (GDA) algorithm that employs both shuffling schemes and variance reduction to solve nonconvex-strongly concave smooth minimax problems. We show that the proposed algorithm achieves $ε$-stationarity in expectation in $\mathcal{O}(κ^2 ε^{-2})$ iterations, where $κ$ is the condition number of the problem. This outperforms existing shuffling schemes and matches the complexity of the best-known sampling-with-replacement algorithms. Our proposed algorithm also achieves the same complexity as that of its deterministic counterpart, the two-timescale GDA algorithm. Our numerical experiments demonstrate the superior performance of the proposed algorithm.

math.OC

Heavy-Ball Momentum Accelerated Actor-Critic With Function Approximation

By using an parametric value function to replace the Monte-Carlo rollouts for value estimation, the actor-critic (AC) algorithms can reduce the variance of stochastic policy gradient so that to improve the convergence rate. While existing works mainly focus on analyzing convergence rate of AC algorithms under Markovian noise, the impacts of momentum on AC algorithms remain largely unexplored. In this work, we first propose a heavy-ball momentum based advantage actor-critic (\mbox{HB-A2C}) algorithm by integrating the heavy-ball momentum into the critic recursion that is parameterized by a linear function. When the sample trajectory follows a Markov decision process, we quantitatively certify the acceleration capability of the proposed HB-A2C algorithm. Our theoretical results demonstrate that the proposed HB-A2C finds an $ε$-approximate stationary point with $\oo{ε^{-2}}$ iterations for reinforcement learning tasks with Markovian noise. Moreover, we also reveal the dependence of learning rates on the length of the sample trajectory. By carefully selecting the momentum factor of the critic recursion, the proposed HB-A2C can balance the errors introduced by the initialization and the stoschastic approximation.

cs.LG

A regularized variance-reduced modified extragradient method for stochastic hierarchical games

We consider an N-player hierarchical game in which the i-th player's objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the virtual power plants, emphasizing the role of hierarchical decision making and regularization.

math.OC

Complexity guarantees for an implicit smoothing-enabled method for stochastic MPECs

Stochastic MPECs have found increasing relevance for modeling a broad range of settings in engineering and statistics. Yet, there seem to be no efficient first/zeroth-order schemes equipped with non-asymptotic rate guarantees for resolving even deterministic variants of such problems. We consider SMPECs where the parametrized lower-level equilibrium problem is given by a deterministic/stochastic VI problem whose mapping is strongly monotone. We develop a zeroth-order implicit algorithmic framework by leveraging a locally randomized spherical smoothing scheme. We present schemes for single-stage and two-stage stochastic MPECs when the upper-level problem is either convex or nonconvex. (I). Single-stage SMPECs: In convex regimes, our proposed inexact schemes are characterized by a complexity in upper-level projections, upper-level samples, and lower-level projections of $\mathcal{O}(\tfrac{1}{ε^2})$, $\mathcal{O}(\tfrac{1}{ε^2})$, and $\mathcal{O}(\tfrac{1}{ε^2}\ln(\tfrac{1}ε))$ , respectively. Analogous bounds for the nonconvex regime are $\mathcal{O}(\tfrac{1}ε)$, $\mathcal{O}(\tfrac{1}{ε^2})$, and $\mathcal{O}(\tfrac{1}{ε^3})$, respectively . (II). Two-stage SMPECs: In convex regimes, our proposed inexact schemes have a complexity in upper-level projections, upper-level samples, and lower-level projections of $\mathcal{O}(\tfrac{1}{ε^2}),\mathcal{O}(\tfrac{1}{ε^2})$, and $\mathcal{O}(\tfrac{1}{ε^2}\ln(\tfrac{1}ε))$ while the corresponding bounds in the nonconvex regime are $\mathcal{O}(\tfrac{1}ε)$, $\mathcal{O}(\tfrac{1}{ε^2})$, and $\mathcal{O}(\tfrac{1}{ε^2}\ln(\tfrac{1}ε))$ , respectively . In addition, we derive statements for exact as well as accelerated counterparts. We also provide a comprehensive set of numerical results for validating the theoretical findings.

math.OC

On the computation of equilibria in monotone and potential stochastic hierarchical games

We consider a class of hierarchical noncooperative $N$-player games where the $i$th player solves a parametrized stochastic mathematical program with equilibrium constraints (MPEC) with the caveat that the implicit form of the $i$th player's in MPEC is convex in player strategy, given rival decisions. We develop computational schemes in two distinct regimes: (a) {\em Monotone regimes.} When player-specific implicit problems are convex, then the necessary and sufficient equilibrium conditions are given by a stochastic inclusion. Under a monotonicity assumption on the operator, we develop a variance-reduced stochastic proximal-point scheme that achieves deterministic rates of convergence in terms of solving proximal-point problems in monotone/strongly monotone regimes and the schemes are characterized by optimal or near-optimal sample-complexity guarantees. (b) {\em Potentiality.} When the implicit form of the game admits a potential function, we develop an asynchronous relaxed inexact smoothed proximal best-response framework. We consider the smoothed counterpart of this game where each player's problem is smoothed via randomized smoothing. Notably, under suitable assumptions, we show that an $η$-smoothed game admits an $η$-approximate Nash equilibrium of the original game. Our proposed scheme produces a sequence that converges almost surely to an $η$-approximate Nash equilibrium. The smoothing framework allows for developing a variance-reduced zeroth-order scheme for such problems that admits a fast rate of convergence. Numerical studies on a class of multi-leader multi-follower games suggest that variance-reduced proximal schemes provide significantly better accuracy with far lower run-times. The relaxed best-response scheme scales well will problem size and generally displays more stability than its unrelaxed counterpart.

math.OC

Variance-Reduced Splitting Schemes for Monotone Stochastic Generalized Equations

We consider monotone inclusion problems where the operators may be expectation-valued, a class of problems that subsumes convex stochastic optimization problems as well as subclasses of stochastic variational inequality and equilibrium problems. A direct application of splitting schemes is complicated by the need to resolve problems with expectation-valued maps at each step, a concern that is addressed by using sampling. Accordingly, we propose an avenue for addressing uncertainty in the mapping: Variance-reduced stochastic modified forward-backward splitting scheme (vr-SMFBS). In constrained settings, we consider structured settings when the map can be decomposed into an expectation-valued map A and a maximal monotone map B with a tractable resolvent. We show that the proposed schemes are equipped with a.s. convergence guarantees, linear (strongly monotone A) and O(1/k) (monotone A) rates of convergence while achieving optimal oracle complexity bounds. The rate statements in monotone regimes appear to be amongst the first and rely on leveraging the Fitzpatrick gap function for monotone inclusions. Furthermore, the schemes rely on weaker moment requirements on noise and allow for weakening unbiasedness requirements on oracles in strongly monotone regimes. Preliminary numerics on a class of two-stage stochastic variational inequality problems reflect these findings and show that the variance-reduced schemes outperform stochastic approximation schemes and sample-average approximation approaches. The benefits of attaining deterministic rates of convergence become even more salient when resolvent computation is expensive.

math.OC

Stochastic Relaxed Inertial Forward-Backward-Forward splitting for Monotone Inclusions in Hilbert spaces

We consider monotone inclusions defined on a Hilbert space where the operator is given by the sum of a maximal monotone operator $T$ and a single-valued monotone, Lipschitz continuous, and expectation-valued operator $V$. We draw motivation from the seminal work by Attouch and Cabot on relaxed inertial methods for monotone inclusions and present a stochastic extension of the relaxed inertial forward-backward-forward (RISFBF) method. Facilitated by an online variance reduction strategy via a mini-batch approach, we show that (RISFBF) produces a sequence that weakly converges to the solution set. Moreover, it is possible to estimate the rate at which the discrete velocity of the stochastic process vanishes. Under strong monotonicity, we demonstrate strong convergence, and give a detailed assessment of the iteration and oracle complexity of the scheme. When the mini-batch is raised at a geometric (polynomial) rate, the rate statement can be strengthened to a linear (suitable polynomial) rate while the oracle complexity of computing an $ε$-solution improves to $O(1/ε)$. Importantly, the latter claim allows for possibly biased oracles, a key theoretical advancement allowing for far broader applicability. By defining a restricted gap function based on the Fitzpatrick function, we prove that the expected gap of an averaged sequence diminishes at a sublinear rate of $O(1/k)$ while the oracle complexity of computing a suitably defined $ε$-solution is $O(1/ε^{1+a})$ where $a>1$. Numerical results on two-stage games and an overlapping group Lasso problem illustrate the advantages of our method compared to stochastic forward-backward-forward (SFBF) and SA schemes.

math.OC

A relaxed-inertial forward-backward-forward algorithm for Stochastic Generalized Nash equilibrium seeking

In this paper we propose a new operator splitting algorithm for distributed Nash equilibrium seeking under stochastic uncertainty, featuring relaxation and inertial effects. Our work is inspired by recent deterministic operator splitting methods, designed for solving structured monotone inclusion problems. The algorithm is derived from a forward-backward-forward scheme for solving structured monotone inclusion problems featuring a Lipschitz continuous and monotone game operator. To the best of our knowledge, this is the first distributed (generalized) Nash equilibrium seeking algorithm featuring acceleration techniques in stochastic Nash games without assuming cocoercivity. Numerical examples illustrate the effect of inertia and relaxation on the performance of our proposed algorithm.

math.OC

On the analysis of variance-reduced and randomized projection variants of single projection schemes for monotone stochastic variational inequality problems

Classical extragradient schemes and their stochastic counterpart represent a cornerstone for resolving monotone variational inequality problems. Yet, such schemes have a per-iteration complexity of two projections onto a convex set and require two evaluations of the map, the former of which could be relatively expensive if $X$ is a complicated set. We consider two related avenues where the per-iteration complexity is significantly reduced: (i) A stochastic projected reflected gradient method requiring a single evaluation of the map and a single projection; and (ii) A stochastic subgradient extragradient method that requires two evaluations of the map, a single projection onto $X$, and a significantly cheaper projection (onto a halfspace) computable in closed form. Under a variance-reduced framework reliant on a sample-average of the map based on an increasing batch-size, we prove almost sure (a.s.) convergence of the iterates to a random point in the solution set for both schemes. Additionally, both schemes display a non-asymptotic rate of $\mathcal{O}(1/K)$ where $K$ denotes the number of iterations; notably, both rates match those obtained in deterministic regimes. To address feasibility sets given by the intersection of a large number of convex constraints, we adapt both of the aforementioned schemes to a random projection framework. We then show that the random projection analogs of both schemes also display a.s. convergence under a weak-sharpness requirement; furthermore, without imposing the weak-sharpness requirement, both schemes are characterized by a provable rate of $\mathcal{O}(1/\sqrt{K})$ in terms of the gap function of the projection of the averaged sequence onto $X$ as well as the infeasibility of this sequence. Preliminary numerics support theoretical findings and the schemes outperform standard extragradient schemes in terms of the per-iteration complexity.

math.OC

Development of modeling and control strategies for an approximated Gaussian process

The Gaussian process (GP) model, which has been extensively applied as priors of functions, has demonstrated excellent performance. The specification of a large number of parameters affects the computational efficiency and the feasibility of implementation of a control strategy. We propose a linear model to approximate GPs; this model expands the GP model by a series of basis functions. Several examples and simulation studies are presented to demonstrate the advantages of the proposed method. A control strategy is provided with the proposed linear model.

stat.ML