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Safe anytime-valid inference (SAVI) provides measures of statistical evidence and certainty -- e-processes for testing and confidence sequences for estimation -- that remain valid at all stopping times, accommodating continuous monitoring…
Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biological models. Informally an ESS is a strategy that if followed by the population cannot be taken over by a…
A sequence of spin-1/2 particles polarised in one of two possible directions is presented to an experimenter, who can wager in a double-or-nothing game on the outcomes of measurements in freely chosen polarisation directions. Wealth is…
We consider a deterministic game with alternate moves and complete information, of which the issue is always the victory of one of the two opponents. We assume that this game is the realization of a random model enjoying some independence…
We study the problem of designing consistent sequential two-sample tests in a nonparametric setting. Guided by the principle of testing by betting, we reframe this task into that of selecting a sequence of payoff functions that maximize the…
In large-scale hypothesis testing, computing exact $p$-values or $e$-values is often resource-intensive, creating a need for budget-aware inferential methods. We propose a general framework for active hypothesis testing that leverages…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
We study the problem of detecting planted solutions in a random satisfiability formula. Adopting the formalism of hypothesis testing in statistical analysis, we describe the minimax optimal rates of detection. Our analysis relies on the…
Pure exploration (aka active testing) is the fundamental task of sequentially gathering information to answer a query about a stochastic environment. Good algorithms make few mistakes and take few samples. Lower bounds (for multi-armed…
Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression. The methodologies rely chiefly on the method of maximizing the…
The idea of approximating the Shapley value of an n-person game by Monte Carlo simulation was first suggested by Mann and Shapley (1960) and they also introduced four different heuristical methods to reduce the estimation error. Since 1960,…
We introduce a new hypothesis testing-based learning dynamics in which players update their strategies by combining hypothesis testing with utility-driven exploration. In this dynamics, each player forms beliefs about opponents' strategies…
We frame the meta-learning of prediction procedures as a search for an optimal strategy in a two-player game. In this game, Nature selects a prior over distributions that generate labeled data consisting of features and an associated…
We consider an N-player hierarchical game in which the i-th player's objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
The composite binary hypothesis testing problem within the Neyman-Pearson framework is considered. The goal is to maximize the expectation of a nonlinear function of the detection probability, integrated with respect to a given probability…
The steadily increasing size of scientific Monte Carlo simulations and the desire for robust, correct, and reproducible results necessitates rigorous testing procedures for scientific simulations in order to detect numerical problems and…
How can we monitor, in real time, whether one uncertain prospect has any upside over another? To answer this question, we develop a novel family of sequential, anytime-valid tests for stochastic dominance (SD; also known as stochastic…
We develop and compare e-variables for testing whether $k$ samples of data are drawn from the same distribution, the alternative being that they come from different elements of an exponential family. We consider the GRO (growth-rate…
Solving an optimization task in any domain is a very challenging problem, especially when dealing with nonlinear problems and non-convex functions. Many meta-heuristic algorithms are very efficient when solving nonlinear functions. A…