相关论文: Blackwell Approachability and Minimax Theory

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…

The literature on ranking from ordinal data is vast, and there are several ways to aggregate overall preferences from pairwise comparisons between objects. In particular, it is well known that any Nash equilibrium of the zero sum game…

Predictive models in ML need to be trustworthy and reliable, which often at the very least means outputting calibrated probabilities. This can be particularly difficult to guarantee in the online prediction setting when the outcome sequence…

This paper investigates probabilistic robustness of nonconvex-nonconcave minimax problems via the scenario approach. Specifically, under convex strategy sets for all players, inspired by recent advances in scenario optimization, we first…

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…

We study the problem of optimizing a graph-structured objective function under \emph{adversarial} uncertainty. This problem can be modeled as a two-persons zero-sum game between an Engineer and Nature. The Engineer controls a subset of the…

In this note, we consider the problem of choosing which nodes of a linear dynamical system should be actuated so that the state transfer from the system's initial condition to a given final state is possible. Assuming a standard complexity…

We discuss the interconnections between AO*, adversarial game-searching algorithms, e.g., proof number search and minimax search. The former was developed in the context of a general AND/OR graph model, while the latter were mostly…

In statistical decision theory involving a single decision-maker, an information structure is said to be better than another one if for any cost function involving a hidden state variable and an action variable which is restricted to be…

This paper uses category theory to develop an entirely new approach to approximate game theory. Game theory is the study of how different agents within a multi-agent system take decisions. At its core, game theory asks what an optimal…

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in $NP \cap coNP$ which are not known to be in $P$. However, there are some…

The equivalence between von Neumann's Minimax Theorem for zero-sum games and the LP Duality Theorem connects cornerstone problems of the two fields of game theory and optimization, respectively, and has been the subject of intense scrutiny…

We study concurrent stochastic reachability games played on finite graphs. Two players, Max and Min, seek respectively to maximize and minimize the probability of reaching a set of target states. We prove that Max has a memoryless strategy…

This paper reframes approachability theory within the context of population games. Thus, whilst one player aims at driving her average payoff to a predefined set, her opponent is not malevolent but rather extracted randomly from a…

We consider concurrent stochastic games played on graphs with reachability and safety objectives. These games can be solved by value iteration as well as strategy iteration, each of them yielding a sequence of under-approximations of the…

This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic…

Motivated by applications in Markov chain Monte Carlo, we discuss what it means for one Markov chain to be an approximation to another. Specifically included in that discussion are situations in which a Markov chain with continuous state…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

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…

We reveal an interesting convex duality relationship between two problems: (a) minimizing the probability of lifetime ruin when the rate of consumption is stochastic and when the individual can invest in a Black-Scholes financial market;…