arXiv research

New algorithm solves minimax games with linear constraints.

Negative momentum accelerates convergence in minimax games but at a suboptimal rate.

Convergence to a saddle point for convex-concave functions has been studied for decades, while recent years has seen a surge of interest in non-convex (zero-sum) smooth games, motivated by their recent wide applications. It remains an intriguing research challenge how local optimal points are defined and which algorith…

Paper explains adversarial training's robust overfitting through a minimax game perspective.

Proves minimax sample complexity for turn-based stochastic games.

Improved FTPL algorithm reduces regret in predictable minimax games.

New algorithms solve nonconvex-nonconcave minimax optimization problems.

Many tasks in modern machine learning can be formulated as finding equilibria in \emph{sequential} games. In particular, two-player zero-sum sequential games, also known as minimax optimization, have received growing interest. It is tempting to apply gradient descent to solve minimax optimization given its popularity a…

We consider the problem of two-player zero-sum games. This problem is formulated as a min-max Markov game in the literature. The solution of this game, which is the min-max payoff, starting from a given state is called the min-max value of the state. In this work, we compute the solution of the two-player zero-sum game…

Alt-GDA outperforms Sim-GDA in minimax games with near-optimal local convergence.

We prove a new minimax theorem connecting the worst-case Bayesian regret and minimax regret under partial monitoring with no assumptions on the space of signals or decisions of the adversary. We then generalise the information-theoretic tools of Russo and Van Roy (2016) for proving Bayesian regret bounds and combine th…

Partial-monitoring games constitute a mathematical framework for sequential decision making problems with imperfect feedback: The learner repeatedly chooses an action, opponent responds with an outcome, and then the learner suffers a loss and receives a feedback signal, both of which are fixed functions of the action a…

New bounds show simple predictors can learn complex concepts online.

Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in reinforcement learning which have been applied to complex games such as Go or Poker. In p…

The paper develops a new algorithm for constructing minimax estimators using online learning techniques.

Unified framework for Bayesian and Frequentist statistics.

Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning. As most of these applications involve continuous nonconvex-nonconcave formulations, a very basic question arises---"w…

We develop a worst-case analysis of aggregation of classifier ensembles for binary classification. The task of predicting to minimize error is formulated as a game played over a given set of unlabeled data (a transductive setting), where prior label information is encoded as constraints on the game. The minimax solutio…

Bayesian methods suffer from the problem of how to specify prior beliefs. One interesting idea is to consider worst-case priors. This requires solving a stochastic zero-sum game. In this paper, we extend well-known results from bandit theory in order to discover minimax-Bayes policies and discuss when they are practica…

Paper finds algorithms with both low regret and high exploitation.

The paper explores the information-theoretic nature of excess risk in machine learning.

We study the problem of switching-constrained online convex optimization (OCO), where the player has a limited number of opportunities to change her action. While the discrete analog of this online learning task has been studied extensively, previous work in the continuous setting has neither established the minimax ra…

Paper learns skill distributions from game outcomes, proving minimax optimality.

We consider a symmetric multi-players zero-sum game with two strategic variables. There are $n$ players, $n\geq 3$. Each player is denoted by $i$. Two strategic variables are $t_i$ and $s_i$, $i\in \{1, \dots, n\}$. They are related by invertible functions. Using the minimax theorem by \cite{sion} we will show that Nas…

We provide a simple and efficient algorithm for adversarial $k$-action $d$-outcome non-degenerate locally observable partial monitoring game for which the $n$-round minimax regret is bounded by $6(d+1) k^{3/2} \sqrt{n \log(k)}$, matching the best known information-theoretic upper bound. The same algorithm also achieves…

New ranking system balances fairness and user utility.

Paper optimizes multi-agent learning in Markov games with generative model.

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and…

Pessimistic Minimax Value Iteration finds efficient NE policies from offline data.

New algorithm AG-OG optimizes separable convex-concave problems efficiently.

New algorithm for offline RL with linear approx in MDPs and MGs, nearly optimal.

New assumptions and algorithm solve offline two-player zero-sum Markov games.

Bidirectional bounds stabilize training of energy-based models.

A game-theoretic approach to multi-criteria ranking from ordinal data.

Study online learning in unknown Markov games with sublinear regret.

Option contracts are a type of financial derivative that allow investors to hedge risk and speculate on the variation of an asset's future market price. In short, an option has a particular payout that is based on the market price for an asset on a given date in the future. In 1973, Black and Scholes proposed a valuati…

Paper analyzes GANs training difficulties and proposes a control framework.

Paper resolves bias in ALFT training using generalized alignment games.

Recently, researchers have discovered that the state-of-the-art object classifiers can be fooled easily by small perturbations in the input unnoticeable to human eyes. It is also known that an attacker can generate strong adversarial examples if she knows the classifier parameters. Conversely, a defender can robustify …

Algorithm learns from changing zero-sum games with no regret.

Study optimizes best-arm identification with minimax and Bayes strategies.

GAT-GMM improves GANs' performance in learning Gaussian mixture models.

State-of-the-art adversarial attacks are aimed at neural network classifiers. By default, neural networks use gradient descent to minimize their loss function. The gradient of a classifier's loss function is used by gradient-based adversarial attacks to generate adversarially perturbed images. We pose the question whet…

We address the online linear optimization problem when the actions of the forecaster are represented by binary vectors. Our goal is to understand the magnitude of the minimax regret for the worst possible set of actions. We study the problem under three different assumptions for the feedback: full information, and the …

Algorithm solves online binary classification and infinite games using ERM oracle.

New algorithm for solving minimax problems over distributions converges to Nash equilibrium.

This paper tackles convex-submodular minimax problems in mixed continuous-discrete domains.

Study tests feasibility of linear programs with bandit feedback.