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The Reward-Penalty-Selection Problem (RPSP) can be seen as a combination of the Set Cover Problem (SCP) and the Hitting Set Problem (HSP). Given a set of elements, a set of reward sets, and a set of penalty sets, one tries to find a subset…

We study a zero-sum game where the evolution of a spectrally one-sided Levy process is modified by a singular controller and is terminated by the stopper. The singular controller minimizes the expected values of running, controlling and…

The loss function used to train a neural network is strongly connected to its output layer from a statistical point of view. This technical report analyzes common activation functions for a neural network output layer, like linear, sigmoid,…

Function approximation is a powerful approach for structuring large decision problems that has facilitated great achievements in the areas of reinforcement learning and game playing. Regression counterfactual regret minimization (RCFR) is a…

Inverse Reinforcement Learning (IRL) aims to facilitate a learner's ability to imitate expert behavior by acquiring reward functions that explain the expert's decisions. Regularized IRL applies strongly convex regularizers to the learner's…

We develop an analytical framework to characterize the set of optimal ReLU neural networks by reformulating the non-convex training problem as a convex program. We show that the global optima of the convex parameterization are given by a…

We establish that randomly initialized neural networks, with large width and a natural choice of hyperparameters, have nearly independent outputs exactly when their activation function is nonlinear with zero mean under the Gaussian measure:…

Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…

Reachability games are two-player games played on a graph, where the objective of $\texttt{REACH}$ player is to reach the target set whereas the objective of $\texttt{SAFE}$ player is to stay away from the target set. Reachability games…

We study when geometric simplicity of decision boundaries, used here as a notion of interpretability, can conflict with accurate approximation of axis-aligned decision trees by shallow neural networks. Decision trees induce rule-based,…

Robust Reinforcement Learning (RRL) is a promising Reinforcement Learning (RL) paradigm aimed at training robust to uncertainty or disturbances models, making them more efficient for real-world applications. Following this paradigm,…

Inverse reinforcement learning (IRL) aims to recover the reward function of an expert agent from demonstrations of behavior. It is well-known that the IRL problem is fundamentally ill-posed, i.e., many reward functions can explain the…

In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…

A recent body of experimental literature has studied empirical game-theoretical analysis, in which we have partial knowledge of a game, consisting of observations of a subset of the pure-strategy profiles and their associated payoffs to…

In the literature on game-theoretic equilibrium finding, focus has mainly been on solving a single game in isolation. In practice, however, strategic interactions -- ranging from routing problems to online advertising auctions -- evolve…

Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative,…

This paper introduces a structural game-theoretic model to value decentralized digital assets like Bitcoin. Instead of relying on speculative beliefs, it frames the asset's price within a Rational-Expectations Security-Utility Nash…

We consider the classic motion planning problem defined over a roadmap in which a vehicle seeks to find an optimal path from a source to a destination in presence of an attacker who can launch attacks on the vehicle over any edge of the…

In an inverse game problem, one needs to infer the cost function of the players in a game such that a desired joint strategy is a Nash equilibrium. We study the inverse game problem for a class of multiplayer matrix games, where the cost…

This paper examines the convergence of no-regret learning in games with continuous action sets. For concreteness, we focus on learning via "dual averaging", a widely used class of no-regret learning schemes where players take small steps…