In reinforcement learning, the standard criterion to evaluate policies in a state is the expectation of (discounted) sum of rewards. However, this criterion may not always be suitable, we consider an alternative criterion based on the notion of quantiles. In the case of episodic reinforcement learning problems, we propose an algorithm based on stochastic approximation with two timescales. We evaluate our proposition on a simple model of the TV show, Who wants to be a millionaire.
Markov decision processes (MDPs) are controllable discrete event systems with stochastic transitions. Performances of an MDP are evaluated by a payoff function. The controller of the MDP seeks to optimize those performances, using optimal strategies. There exists various ways of measuring performances, i.e. various classes of payoff functions. For example, average performances can be evaluated by a mean-payoff function, peak performances by a limsup payoff function, and the parity payoff function can be used to encode logical specifications. Surprisingly, all the MDPs equipped with mean, limsup or parity payoff functions share a common non-trivial property: they admit pure stationary optimal strategies. In this paper, we introduce the class of prefix-independent and submixing payoff functions, and we prove that any MDP equipped with such a payoff function admits pure stationary optimal strategies. This result unifies and simplifies several existing proofs. Moreover, it is a key tool for generating new examples of MDPs with pure stationary optimal strategies. This paper is devoted to sequential decision making under uncertainty, in the multi-prior framework of Gilboa and Schmeidler [1989]. In this setting, a set of probability measures (priors) is defined instead of a single one, and the decision maker selects a strategy that maximizes the minimum possible value of expected utility over this set of priors. We are interested here in the resolute choice approach, where one initially commits to a complete strategy and never deviates from it later. Given a decision tree representation with multiple priors, we study the problem of determining an optimal strategy from the root according to min expected utility. We prove the intractability of evaluating a strategy in the general case. We then identify different properties of a decision tree that enable to design dedicated resolution procedures. Finally, experimental results are presented that evaluate these procedures.