Related papers: A coding theoretic study of homogeneous Markovian …
This paper gives game-theoretic versions of several results on "merging of opinions" obtained in measure-theoretic probability and algorithmic randomness theory. An advantage of the game-theoretic versions over the measure-theoretic results…
This article continues study of the prequential framework for evaluating a probability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using…
This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for…
In late May of 2014 I received an email from a colleague introducing to me a non-transitive game developed by Walter Penney. This paper explores this probability game from the perspective of a coin tossing game, and further discusses some…
Planning safe robot motions in the presence of humans requires reliable forecasts of future human motion. However, simply predicting the most likely motion from prior interactions does not guarantee safety. Such forecasts fail to model the…
One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning…
We propose an original model for inferring team strengths using a Markov Random Field, which can be used to generate historical estimates of the offensive and defensive strengths of a team over time. This model was designed to be applied to…
We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding…
This paper formally models the strategic repeated interactions between a system, comprising of a machine learning (ML) model and associated explanation method, and an end-user who is seeking a prediction/label and its explanation for a…
In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove…
A large body of research is currently investigating on the connection between machine learning and game theory. In this work, game theory notions are injected into a preference learning framework. Specifically, a preference learning problem…
We propose a betting strategy based on Bayesian logistic regression modeling for the probability forecasting game in the framework of game-theoretic probability by Shafer and Vovk (2001). We prove some results concerning the strong law of…
Collective intelligence emerges across biological, physical, and artificial systems without central coordination, yet a unifying principle governing such behaviour remains elusive. The Free Energy Principle explains how individual agents…
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.…
Using the game-theoretic framework for probability, Vovk and Shafer. have shown that it is always possible, using randomization, to make sequential probability forecasts that pass any countable set of well-behaved statistical tests. This…
Coding theory revolves around the incorporation of redundancy into transmitted symbols, computation tasks, and stored data to guard against adversarial manipulation. However, error correction in coding theory is contingent upon a strict…
We begin by reviewing and proving the basic facts of combinatorial game theory. We then consider scoring games (also known as Milnor games or positional games), focusing on the "fixed-length" games for which all sequences of play terminate…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
The dynamics in games involving multiple players, who adaptively learn from their past experience, is not yet well understood. We analyzed a class of stochastic games with Markov strategies in which players choose their actions…
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…