Related papers: The Gambler's Problem and Beyond

Sequences of repeated gambles provide an experimental tool to characterize the risk preferences of humans or artificial decision-making agents. The difficulty of this inference depends on factors including the details of the gambles offered…

The iterated prisoner's dilemma is a game that produces many counter-intuitive and complex behaviors in a social environment, based on very simple basic rules. It illustrates that cooperation can be a good thing even in a competitive world,…

We study two player reachability-price games on single-clock timed automata. The problem is as follows: given a state of the automaton, determine whether the first player can guarantee reaching one of the designated goal locations. If a…

We introduce the concept of attainable sets of payoffs in two-player repeated games with vector payoffs. A set of payoff vectors is called {\em attainable} if player 1 can ensure that there is a finite horizon $T$ such that after time $T$…

We study optimal portfolio choice models in markets with partial information about the stock's drift. We solve the single agent problem for general utilities using a new approach that yields regularity of the value function and closed form…

We construct a diffusion approximation of a repeated game in which agents make bets on outcomes of i.i.d. random vectors and their strategies are close to an asymptotically optimal strategy. This model can be interpreted as trading in an…

We study the problem of designing autonomous agents that can learn to cooperate effectively with a potentially suboptimal partner while having no access to the joint reward function. This problem is modeled as a cooperative episodic…

This article studies inverse reinforcement learning (IRL) for the stochastic linear-quadratic optimal control problem, where two agents are considered. A learner agent does not know the expert agent's performance cost function, but it…

We propose a reinforcement learning (RL) approach to model optimal exercise strategies for option-type products. We pursue the RL avenue in order to learn the optimal action-value function of the underlying stopping problem. In addition to…

In this work, we address the problem of determining reliable policies in reinforcement learning (RL), with a focus on optimization under uncertainty and the need for performance guarantees. While classical RL algorithms aim at maximizing…

This paper is a continuation of Ishitani and Kato (2015), in which we derived a continuous-time value function corresponding to an optimal execution problem with uncertain market impact as the limit of a discrete-time value function. Here,…

Many poker systems, whether created with heuristics or machine learning, rely on the probability of winning as a key input. However calculating the precise probability using combinatorics is an intractable problem, so instead we approximate…

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the…

Value-function-based methods have long played an important role in reinforcement learning. However, finding the best next action given a value function of arbitrary complexity is nontrivial when the action space is too large for…

Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion -- almost everywhere computable randomness. A binary sequence…

Recommending a sequence of activities for an ongoing case requires that the recommendations conform to the underlying business process and meet the performance goal of either completion time or process outcome. Existing work on next…

Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior…

There exist a number of reinforcement learning algorithms which learnby climbing the gradient of expected reward. Their long-runconvergence has been proved, even in partially observableenvironments with non-deterministic actions, and…

For two-person dynamic zero-sum games (both discrete and continuous settings), we investigate the limit of value functions of finite horizon games with long run average cost as the time horizon tends to infinity and the limit of value…

We show that when a third party, the adversary, steps into the two-party setting (agent and operator) of safely interruptible reinforcement learning, a trade-off has to be made between the probability of following the optimal policy in the…