Related papers: Testing exchangeability by pairwise betting

Suppose that at any stage of a statistical experiment a control variable $X$ that affects the distribution of the observed data $Y$ can be used. The distribution of $Y$ depends on some unknown parameter $\theta$, and we consider the…

Conformal prediction has been a very popular method of distribution-free predictive inference in recent years in machine learning and statistics. Its popularity stems from the fact that it works as a wrapper around any prediction algorithm…

Probabilistic model checking for stochastic games enables formal verification of systems that comprise competing or collaborating entities operating in a stochastic environment. Despite good progress in the area, existing approaches focus…

The problem of efficient sharing of a resource is nearly ubiquitous. Except for pure public goods, each agent's use creates a negative externality; often the negative externality is so strong that efficient sharing is impossible in the…

The actions of intelligent agents, such as chatbots, recommender systems, and virtual assistants are typically not fully transparent to the user. Consequently, using such an agent involves the user exposing themselves to the risk that the…

This paper coins the notion of Joker games, a variant of concurrent games where the players are not strictly adversarial. Instead, Player 1 can get help from Player 2 by playing a Joker move. We formalize these games as cost games and…

We propose a general framework for constructing powerful, sequential hypothesis tests for a large class of nonparametric testing problems. The null hypothesis for these problems is defined in an abstract form using the action of two known…

We study environments in which agents are randomly matched to play a Prisoner's Dilemma, and each player observes a few of the partner's past actions against previous opponents. We depart from the existing related literature by allowing a…

Information in the form of data, which can be stored and transferred between users, can be viewed as an intangible commodity, which can be traded in exchange for money. Determining the fair price at which a string of data should be traded…

We give operational meaning to wave-particle duality in terms of discrimination games. Duality arises as a constraint on the probability of winning these games. The games are played with the aid of an n-port interferometer, and involve 3…

Probability forecasts for binary events play a central role in many applications. Their quality is commonly assessed with proper scoring rules, which assign forecasts a numerical score such that a correct forecast achieves a minimal…

We consider parity games on infinite graphs where configurations are represented by control-states and integer vectors. This framework subsumes two classic game problems: parity games on vector addition systems with states (vass) and…

This paper derives confidence intervals (CI) and time-uniform confidence sequences (CS) for the classical problem of estimating an unknown mean from bounded observations. We present a general approach for deriving concentration bounds, that…

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…

This paper studies a system security problem in the context of observability based on a two-person noncooperative infinitely repeated game. Both the attacker and the defender have means to modify the dimension of the unobservable subspace,…

Gambles are random variables that model possible changes in monetary wealth. Classic decision theory transforms money into utility through a utility function and defines the value of a gamble as the expectation value of utility changes.…

We consider the problem of estimating `preference' or `strength' parameters in three-way comparison experiments, each composed of a series of paired comparisons, but where only the single `preferred' or `strongest' candidate is known in…

We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a)…

Suppose that the outcomes of a roulette table are not entirely random, in the sense that there exists a successful betting strategy. Is there a successful `separable' strategy, in the sense that it does not use the winnings from betting on…

We introduce a two-player contest for evaluating the safety and robustness of machine learning systems, with a large prize pool. Unlike most prior work in ML robustness, which studies norm-constrained adversaries, we shift our focus to…