Related papers: Enabling First-Order Gradient-Based Learning for E…

Under mild regularity conditions, gradient-based methods converge globally to a critical point in the single-loss setting. This is known to break down for vanilla gradient descent when moving to multi-loss optimization, but can we hope to…

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…

Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…

Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational and econometric challenges to further improve both model solution and…

We study reinforcement learning in hybrid discrete-continuous action spaces, such as settings where the discrete component selects a regime (or index) and the continuous component optimizes within it -- a structure common in robotics,…

We consider stochastic optimization when one only has access to biased stochastic oracles of the objective and the gradient, and obtaining stochastic gradients with low biases comes at high costs. This setting captures various optimization…

This paper proposes a new mathematical paradigm to analyze discrete-time mean-field games. It is shown that finding Nash equilibrium solutions for a general class of discrete-time mean-field games is equivalent to solving an optimization…

This paper develops the first policy gradient method with global optimality guarantee and complexity analysis for robust reinforcement learning under model mismatch. Robust reinforcement learning is to learn a policy robust to model…

Variational inequalities have recently attracted considerable interest in machine learning as a flexible paradigm for models that go beyond ordinary loss function minimization (such as generative adversarial networks and related deep…

Risk minimization for nonsmooth nonconvex problems naturally leads to first-order sampling or, by an abuse of terminology, to stochastic subgradient descent. We establish the convergence of this method in the path-differentiable case and…

Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…

We design a simple ascending-price algorithm to compute a $(1+\varepsilon)$-approximate equilibrium in Arrow-Debreu exchange markets with weak gross substitute (WGS) property, which runs in time polynomial in market parameters and $\log…

This work is devoted to solving the composite optimization problem with the mixture oracle: for the smooth part of the problem, we have access to the gradient, and for the non-smooth part, only the one-point zero-order oracle is available.…

This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost function. We develop an approach to track the optimal solution with a bounded error. Unlike the…

Mean field equilibrium (MFE) has emerged as a computationally tractable solution concept for large dynamic games. However, computing MFE remains challenging due to nonlinearities and the absence of contraction properties, limiting its…

Behavioral diversity, expert imitation, fairness, safety goals and others give rise to preferences in sequential decision making domains that do not decompose additively across time. We introduce the class of convex Markov games that allow…

We consider a class of smooth $N$-player noncooperative games, where player objectives are expectation-valued and potentially nonconvex. In such a setting, we consider the largely open question of efficiently computing a suitably defined…

We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…

Balancing convergence speed, generalization capability, and computational efficiency remains a core challenge in deep learning optimization. First-order gradient descent methods, epitomized by stochastic gradient descent (SGD) and Adam,…