In Reinforcement Learning, the performance of learning agents is highly sensitive to the choice of time discretization. Agents acting at high frequencies have the best control opportunities, along with some drawbacks, such as possible inefficient exploration and vanishing of the action advantages. The repetition of the actions, i.e., action persistence, comes into help, as it allows the agent to visit wider regions of the state space and improve the estimation of the action effects. In this work, we derive a novel operator, the All-Persistence Bellman Operator, which allows an effective use of both the low-persistence experience, by decomposition into sub-transition, and the high-persistence experience, thanks to the introduction of a suitable bootstrap procedure. In this way, we employ transitions collected at any time scale to update simultaneously the action values of the considered persistence set. We prove the contraction property of the All-Persistence Bellman Operator and, based on it, we extend classic Q-learning and DQN. After providing a study on the effects of persistence, we experimentally evaluate our approach in both tabular contexts and more challenging frameworks, including some Atari games.

The choice of the control frequency of a system has a relevant impact on the ability of reinforcement learning algorithms to learn a highly performing policy. In this paper, we introduce the notion of action persistence that consists in the repetition of an action for a fixed number of decision steps, having the effect of modifying the control frequency. We start analyzing how action persistence affects the performance of the optimal policy, and then we present a novel algorithm, Persistent Fitted Q-Iteration (PFQI), that extends FQI, with the goal of learning the optimal value function at a given persistence. After having provided a theoretical study of PFQI and a heuristic approach to identify the optimal persistence, we present an experimental campaign on benchmark domains to show the advantages of action persistence and proving the effectiveness of our persistence selection method.

The use of reinforcement learning in algorithmic trading is of growing interest, since it offers the opportunity of making profit through the development of autonomous artificial traders, that do not depend on hard-coded rules. In such a framework, keeping uncertainty under control is as important as maximizing expected returns. Risk aversion has been addressed in reinforcement learning through measures related to the distribution of returns. However, in trading it is essential to keep under control the risk of portfolio positions in the intermediate steps. In this paper, we define a novel measure of risk, which we call reward volatility, consisting of the variance of the rewards under the state-occupancy measure. This new risk measure is shown to bound the return variance so that reducing the former also constrains the latter. We derive a policy gradient theorem with a new objective function that exploits the mean-volatility relationship. Furthermore, we adapt TRPO, the well-known policy gradient algorithm with monotonic improvement guarantees, in a risk-averse manner. Finally, we test the proposed approach in two financial environments using real market data.