Related papers: Limited-Memory LRSGA: An Iterative Method for Comp…

Many important real-world settings contain multiple players interacting over an unknown duration with probabilistic state transitions, and are naturally modeled as stochastic games. Prior research on algorithms for stochastic games has…

An increasing number of machine learning problems, such as robust or adversarial variants of existing algorithms, require minimizing a loss function that is itself defined as a maximum. Carrying a loop of stochastic gradient ascent (SGA)…

This paper proposes a novel approach for local convergence to Nash equilibrium in quadratic noncooperative games based on a distributed Lie-bracket extremum seeking control scheme. This is the first instance of noncooperative games being…

Accelerator memory and networking constraints have emerged as dominant bottlenecks when training large language models LLMs with billions of parameters. Existing low rank gradient estimators such as GaLoRE and FLORA compress gradients and…

Stochastic games have become a prevalent framework for studying long-term multi-agent interactions, especially in the context of multi-agent reinforcement learning. In this work, we comprehensively investigate the concept of constant-memory…

In this tutorial, we provide an introduction to machine learning methods for finding Nash equilibria in games with large number of agents. These types of problems are important for the operations research community because of their…

In zero-sum games, the optimal strategy is well-defined by the Nash equilibrium. However, it is overly conservative when playing against suboptimal opponents and it can not exploit their weaknesses. Limited look-ahead game solving in…

Regret matching (RM) -- and its modern variants -- is a foundational online algorithm that has been at the heart of many AI breakthrough results in solving benchmark zero-sum games, such as poker. Yet, surprisingly little is known so far in…

Feedback Nash equilibrium strategies in multi-agent dynamic games require availability of all players' state information to compute control actions. However, in real-world scenarios, sensing and communication limitations between agents make…

Deep neural networks suffer from catastrophic forgetting when learning multiple knowledge sequentially, and a growing number of approaches have been proposed to mitigate this problem. Some of these methods achieved considerable performance…

We revisit the stochastic limited-memory BFGS (L-BFGS) algorithm. By proposing a new framework for the convergence analysis, we prove improved convergence rates and computational complexities of the stochastic L-BFGS algorithms compared to…

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the…

We consider a distributed stochastic approximation (SA) scheme for computing an equilibrium of a stochastic Nash game. Standard SA schemes employ diminishing steplength sequences that are square summable but not summable. Such requirements…

Large Language Models have shown remarkable capabilities in the NLP domain. Their effectiveness can mainly be attributed to their ability to adapt to an array of downstream tasks. However, generally, full fine-tuning is a computationally…

Continual learning is inherently a constrained learning problem. The goal is to learn a predictor under a no-forgetting requirement. Although several prior studies formulate it as such, they do not solve the constrained problem explicitly.…

Mean field games (MFG) and mean field control problems (MFC) are frameworks to study Nash equilibria or social optima in games with a continuum of agents. These problems can be used to approximate competitive or cooperative games with a…

This paper studies random reshuffling (RR)-based distributed Nash equilibrium seeking for noncooperative games. The game is motivated as a sample-average approximation of an underlying expected-value stochastic game, while the algorithmic…

The enormous parameter scale of large language models (LLMs) has made model compression a research hotspot, which aims to alleviate computational resource demands during deployment and inference. As a promising direction, low-rank…

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac-Frenkel…

Large-scale machine learning models are trained on clusters of machines that exhibit heterogeneous performance due to hardware variability, network delays, and system-level instabilities. In such environments, time complexity rather than…