相关论文: The Gambler's Problem and Beyond

We revisit Blackwell's celebrated approachability problem which considers a repeated vector-valued game between a player and an adversary. Motivated by settings in which the action set of the player or adversary (or both) is difficult to…

The main objective of this paper is to look from the unique point of view at some phenomena arising in different areas of probability theory and mathematical statistics. We will try to understand what is common between classical…

Function approximation (FA) has been a critical component in solving large zero-sum games. Yet, little attention has been given towards FA in solving \textit{general-sum} extensive-form games, despite them being widely regarded as being…

Consider a 2-player normal-form game repeated over time. We introduce an adaptive learning procedure, where the players only observe their own realized payoff at each stage. We assume that agents do not know their own payoff function, and…

In reinforcement learning the Q-values summarize the expected future rewards that the agent will attain. However, they cannot capture the epistemic uncertainty about those rewards. In this work we derive a new Bellman operator with…

We study the exploration problem with approximate linear action-value functions in episodic reinforcement learning under the notion of low inherent Bellman error, a condition normally employed to show convergence of approximate value…

This paper extends the reinforcement learning ideas into the multi-agents system, which is far more complicated than the previously studied single-agent system. We studied two different multi-agents systems. One is the fully-connected…

In some agent designs like inverse reinforcement learning an agent needs to learn its own reward function. Learning the reward function and optimising for it are typically two different processes, usually performed at different stages. We…

We develop value iteration-based algorithms to solve in a unified manner different classes of combinatorial zero-sum games with mean-payoff type rewards. These algorithms rely on an oracle, evaluating the dynamic programming operator up to…

We consider the following combinatorial two-player game: On the random tree arising from a branching process, each round one player (Breaker) deletes an edge and by that removes the descendant and all its progeny, while the other (Maker)…

We study the problem of Reinforcement Learning (RL) with linear function approximation, i.e. assuming the optimal action-value function is linear in a known $d$-dimensional feature mapping. Unfortunately, however, based on only this…

Successful teaching requires an assumption of how the learner learns - how the learner uses experiences from the world to update their internal states. We investigate what expectations people have about a learner when they teach them in an…

We consider a random walk in a truncated cone $K_N$, which is obtained by slicing cone $K$ by a hyperplane at a growing level of order $N$. We study the behaviour of the Green function in this truncated cone as $N$ increases. Using these…

We show that if either the process is strong Feller and the boundary point is probabilistically regular for the stopping set, or the process is strong Markov and the boundary point is probabilistically regular for the interior of the…

Commonly in reinforcement learning (RL), rewards are discounted over time using an exponential function to model time preference, thereby bounding the expected long-term reward. In contrast, in economics and psychology, it has been shown…

As reinforcement learning algorithms are being applied to increasingly complicated and realistic tasks, it is becoming increasingly difficult to solve such problems within a practical time frame. Hence, we focus on a \textit{satisficing}…

The use of reinforcement learning algorithms in financial trading is becoming increasingly prevalent. However, the autonomous nature of these algorithms can lead to unexpected outcomes that deviate from traditional game-theoretical…

We study the Online Bookmaking problem, where a bookmaker dynamically updates betting odds on the possible outcomes of an event. In each betting round, the bookmaker can adjust the odds based on the cumulative betting behavior of gamblers,…

The development of reinforced learning methods has extended application to many areas including algorithmic trading. In this paper trading on the stock exchange is interpreted into a game with a Markov property consisting of states,…

We make progress in a long-standing problem of batch reinforcement learning (RL): learning $Q^\star$ from an exploratory and polynomial-sized dataset, using a realizable and otherwise arbitrary function class. In fact, all existing…