The supplementary material presented here first presents a detailed description of the MCCFR algorithm. We then give proofs to Theorems 3, 4, and 5 from the submission Monte Carlo Sampling for Regret Minimization in Extensive Games. We begin with some preliminaries, then prove a general result about all members of the MCCFR family of algorithms (Theorem 18 in Section 6). We then use that result...

We study a two-player zero-sum game (matrix for short) with the objective of finding saddle point and its value. develop novel convolutional neural network (CNN approach to achieve goal. propose complete training pipeline, including specific CNN model structure handle varying sizes, generating datasets, fitting. The experiment results show that our proposed method outperforms traditional linear...

We consider the pricing problem faced by a monopolist who sells a product to a population of consumers over a finite time horizon. Customers are heterogeneous along two dimensions: (i) willingness-to-pay for the product and (ii) arrival time during the selling season. We assume that the seller knows only the support of the customers’ valuations and do not make any other distributional assumptio...

First, we study online learning with an extended notion of regret, which is defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and deriving efficient learning algorithms in this scenario. While the standard methods for minimizing the usual notion of regret fail, through our analysis we demonstrate the existence of regret-minimization methods that compe...