Related papers: Numerical solution of a PDE arising from predictio…
Predicting the outcomes of future events is a challenging problem for which a variety of solution methods have been explored and attempted. We present an empirical comparison of a variety of online and offline adaptive algorithms for…
We present a robust framework with computational algorithms to support decision makers in sequential games. Our framework includes methods to solve games with complete information, assess the robustness of such solutions and, finally,…
In this paper, we consider convex stochastic optimization problems arising in machine learning applications (e.g., risk minimization) and mathematical statistics (e.g., maximum likelihood estimation). There are two main approaches to solve…
In this paper, we consider an unconstrained distributed optimization problem over a network of agents, in which some agents are adversarial. We solve the problem via gradient-based distributed optimization algorithm and characterize the…
We study online optimization methods for zero-sum games, a fundamental problem in adversarial learning in machine learning, economics, and many other domains. Traditional methods approximate Nash equilibria (NE) using either regret-based…
We formulate and analyze a goal-oriented adaptive finite element method for a symmetric linear elliptic partial differential equation (PDE) that can simultaneously deal with multiple linear goal functionals. In each step of the algorithm,…
This paper presents an efficient algorithm to solve the sleeping bandit with multiple plays problem in the context of an online recommendation system. The problem involves bounded, adversarial loss and unknown i.i.d. distributions for arm…
Computing equilibria of games is a central task in computer science. A large number of results are known for \emph{Nash equilibrium} (NE). However, these can be adopted only when coalitions are not an issue. When instead agents can form…
We study the nascent setting of online computation with imperfect advice, in which the online algorithm is enhanced by some prediction encoded in the form of a possibly erroneous binary string. The algorithm is oblivious to the advice…
In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online…
While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…
We initiate the systematic study of decision-theoretic metrics in the design and analysis of algorithms with machine-learned predictions. We introduce approaches based on both deterministic measures such as distance-based evaluation, that…
We consider the problem of constructing probabilistic predictions that lead to accurate decisions when employed by downstream users to inform actions. For a single decision maker, designing an optimal predictor is equivalent to minimizing a…
In this work, we introduce a novel strategy for tackling constrained optimization problems through a modified penalty method. Conventional penalty methods convert constrained problems into unconstrained ones by incorporating constraints…
This paper considers linear quadratic team decision problems where the players in the team affect each other's information structure through their decisions. Whereas the stochastic version of the problem is well known to be complex with…
In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…
In this paper, the elliptic PDE-constrained optimization problem with box constraints on the control is studied. To numerically solve the problem, we apply the 'optimize-discretize-optimize' strategy. Specifically, the alternating direction…
We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…
The goal of agents in multi-agent environments is to maximize total reward against the opposing agents that are encountered. Following a game-theoretic solution concept, such as Nash equilibrium, may obtain a strong performance in some…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…