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We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games to a concurrent setting where the two players choose moves simultaneously and independently at each state. For…
Stochastic variational inequalities (SVI) model a large class of equilibrium problems subject to data uncertainty, and are closely related to stochastic optimization problems. The SVI solution is usually estimated by a solution to a sample…
Chance constrained optimization problems allow to model problems where constraints involving stochastic components should only be violated with a small probability. Evolutionary algorithms have been applied to this scenario and shown to…
Stochastic Gradient Boosting (SGB) is a widely used approach to regularization of boosting models based on decision trees. It was shown that, in many cases, random sampling at each iteration can lead to better generalization performance of…
When looking for a solution, deterministic methods have the enormous advantage that they do find global optima. Unfortunately, they are very CPU-intensive, and are useless on untractable NP-hard problems that would require thousands of…
We address two-player general-sum stochastic Stackelberg games (SSGs), where the leader's policy is optimized considering the best-response follower whose policy is optimal for its reward under the leader. Existing policy gradient and value…
Like many numerical methods, solvers for initial value problems (IVPs) on ordinary differential equations estimate an analytically intractable quantity, using the results of tractable computations as inputs. This structure is closely…
This paper presents a new exponential lower bound for the two most popular deterministic variants of the strategy improvement algorithms for solving parity, mean payoff, discounted payoff and simple stochastic games. The first variant…
We propose efficient methods for solving stochastic simple bilevel optimization problems with convex inner levels, where the goal is to minimize an outer stochastic objective function subject to the solution set of an inner stochastic…
Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods,…
We study a stochastic variant of the Team Orienteering Problem with lognormal travel times and an all-or-nothing reward policy, under which the reward of a route is lost if its travel time exceeds the available budget. We propose a…
We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical…
Motivated by multi-user optimization problems and non-cooperative Nash games in uncertain regimes, we consider stochastic Cartesian variational inequalities (SCVI) where the set is given as the Cartesian product of a collection of component…
Two standard algorithms for approximately solving two-player zero-sum concurrent reachability games are value iteration and strategy iteration. We prove upper and lower bounds of 2^(m^(Theta(N))) on the worst case number of iterations…
Graph games provide the foundation for modeling and synthesizing reactive processes. In the synthesis of stochastic reactive processes, the traditional model is perfect-information stochastic games, where some transitions of the game graph…
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of…
A recent article introduced thecontinuous stochastic gradient method (CSG) for the efficient solution of a class of stochastic optimization problems. While the applicability of known stochastic gradient type methods is typically limited to…
The focus of this paper is on stochastic variational inequalities (VI) under Markovian noise. A prominent application of our algorithmic developments is the stochastic policy evaluation problem in reinforcement learning. Prior…
We analyze algorithms for solving stochastic variational inequalities (VI) without the bounded variance or bounded domain assumptions, where our main focus is min-max optimization with possibly unbounded constraint sets. We focus on two…
The singular value decomposition (SVD) is a powerful tool in modern numerical linear algebra, which underpins computational methods such as principal component analysis (PCA), low-rank approximations, and randomized algorithms. Many…