Related papers: Learning Approximate Solutions to Multiparametric …

Solving high dimensional partial differential equations (PDEs) has historically posed a considerable challenge when utilizing conventional numerical methods, such as those involving domain meshes. Recent advancements in the field have seen…

The generalized Nash equilibrium problems play a significant role in modeling and analyzing several complex economics problems. In this work, we consider jointly convex generalized Nash games which were introduced by Rosen. We study two…

Solving partial differential equations (PDEs) is a central task in scientific computing. Recently, neural network approximation of PDEs has received increasing attention due to its flexible meshless discretization and its potential for…

Cascading multiple pre-trained models is an effective way to compose an end-to-end system. However, fine-tuning the full cascaded model is parameter and memory inefficient and our observations reveal that only applying adapter modules on…

Multi-agent imitation learning (MA-IL) aims to learn optimal policies from expert demonstrations of interactions in multi-agent interactive domains. Despite existing guarantees on the performance of the resulting learned policies,…

We present a new, distributed method to compute approximate Nash equilibria in bimatrix games. In contrast to previous approaches that analyze the two payoff matrices at the same time (for example, by solving a single LP that combines the…

We explore the use of policy approximations to reduce the computational cost of learning Nash equilibria in zero-sum stochastic games. We propose a new Q-learning type algorithm that uses a sequence of entropy-regularized soft policies to…

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

Deep neural networks (DNNs) are typically optimized using various forms of mini-batch gradient descent algorithm. A major motivation for mini-batch gradient descent is that with a suitably chosen batch size, available computing resources…

In Evolutionary Game Theory (EGT), a population reaches a Nash equilibrium when none of the agents can improve its objective by solely changing its strategy on its own. Roughly speaking, this equilibrium is a protection against betrayal.…

This paper concerns the generalized Nash equilibrium problem of polynomials (GNEPP). We apply the Gauss-Seidel method and Lasserre type Moment-SOS relaxations to solve GNEPPs. The convergence of the Gauss-Seidel method is known for some…

Training deep neural networks for solving machine learning problems is one great challenge in the field, mainly due to its associated optimisation problem being highly non-convex. Recent developments have suggested that many training…

In this work, we propose Natural Hypergradient Descent (NHGD), a new method for solving bilevel optimization problems. To address the computational bottleneck in hypergradient estimation--namely, the need to compute or approximate Hessian…

Large Neighborhood Search (LNS) is a combinatorial optimization heuristic that starts with an assignment of values for the variables to be optimized, and iteratively improves it by searching a large neighborhood around the current…

In this paper, the problem of finding a generalized Nash equilibrium (GNE) of a networked game is studied. Players are only able to choose their decisions from a feasible action set. The feasible set is considered to be a private linear…

Recent progress in deep learning has been driven by increasingly larger models. However, their computational and energy demands have grown proportionally, creating significant barriers to their deployment and to a wider adoption of deep…

Within machine learning, the subfield of Neural Architecture Search (NAS) has recently garnered research attention due to its ability to improve upon human-designed models. However, the computational requirements for finding an exact…

Physics-Informed Neural Networks (PINNs) are mesh-free approaches for the numerical approximation of partial differential equations, where a neural network is trained by minimizing a loss function derived from the governing equations and…

NashOpt is an open-source Python library for computing and designing generalized Nash equilibria (GNEs) in noncooperative games with shared constraints and real-valued decision variables. The library exploits the joint Karush-Kuhn-Tucker…

Regret minimization methods are a powerful tool for learning approximate Nash equilibrium (NE) in two-player zero-sum imperfect information extensive-form games (IIEGs). We consider the problem in the interactive bandit-feedback setting…