Many real-world settings involve costs for performing actions; transaction costs in financial systems and fuel costs being common examples. In these settings, performing actions at each time step quickly accumulates costs leading to vastly suboptimal outcomes. Additionally, repeatedly acting produces wear and tear and ultimately, damage. Determining \textit{when to act} is crucial for achieving successful outcomes and yet, the challenge of efficiently \textit{learning} to behave optimally when actions incur minimally bounded costs remains unresolved. In this paper, we introduce a reinforcement learning (RL) framework named \textbf{L}earnable \textbf{I}mpulse \textbf{C}ontrol \textbf{R}einforcement \textbf{A}lgorithm (LICRA), for learning to optimally select both when to act and which actions to take when actions incur costs. At the core of LICRA is a nested structure that combines RL and a form of policy known as \textit{impulse control} which learns to maximise objectives when actions incur costs. We prove that LICRA, which seamlessly adopts any RL method, converges to policies that optimally select when to perform actions and their optimal magnitudes. We then augment LICRA to handle problems in which the agent can perform at most $k<\infty$ actions and more generally, faces a budget constraint. We show LICRA learns the optimal value function and ensures budget constraints are satisfied almost surely. We demonstrate empirically LICRA's superior performance against benchmark RL methods in OpenAI gym's \textit{Lunar Lander} and in \textit{Highway} environments and a variant of the Merton portfolio problem within finance.

Reinforcement learning (RL) involves performing exploratory actions in an unknown system. This can place a learning agent in dangerous and potentially catastrophic system states. Current approaches for tackling safe learning in RL simultaneously trade-off safe exploration and task fulfillment. In this paper, we introduce a new generation of RL solvers that learn to minimise safety violations while maximising the task reward to the extent that can be tolerated by the safe policy. Our approach introduces a novel two-player framework for safe RL called Distributive Exploration Safety Training Algorithm (DESTA). The core of DESTA is a game between two adaptive agents: Safety Agent that is delegated the task of minimising safety violations and Task Agent whose goal is to maximise the environment reward. Specifically, Safety Agent can selectively take control of the system at any given point to prevent safety violations while Task Agent is free to execute its policy at any other states. This framework enables Safety Agent to learn to take actions at certain states that minimise future safety violations, both during training and testing time, while Task Agent performs actions that maximise the task performance everywhere else. Theoretically, we prove that DESTA converges to stable points enabling safety violations of pretrained policies to be minimised. Empirically, we show DESTA's ability to augment the safety of existing policies and secondly, construct safe RL policies when the Task Agent and Safety Agent are trained concurrently. We demonstrate DESTA's superior performance against leading RL methods in Lunar Lander and Frozen Lake from OpenAI gym.

Satisfying safety constraints almost surely (or with probability one) can be critical for deployment of Reinforcement Learning (RL) in real-life applications. For example, plane landing and take-off should ideally occur with probability one. We address the problem by introducing Safety Augmented (Saute) Markov Decision Processes (MDPs), where the safety constraints are eliminated by augmenting them into the state-space and reshaping the objective. We show that Saute MDP satisfies the Bellman equation and moves us closer to solving Safe RL with constraints satisfied almost surely. We argue that Saute MDP allows to view Safe RL problem from a different perspective enabling new features. For instance, our approach has a plug-and-play nature, i.e., any RL algorithm can be "sauteed". Additionally, state augmentation allows for policy generalization across safety constraints. We finally show that Saute RL algorithms can outperform their state-of-the-art counterparts when constraint satisfaction is of high importance.

We consider a context-dependent Reinforcement Learning (RL) setting, which is characterized by: a) an unknown finite number of not directly observable contexts; b) abrupt (discontinuous) context changes occurring during an episode; and c) Markovian context evolution. We argue that this challenging case is often met in applications and we tackle it using a Bayesian approach and variational inference. We adapt a sticky Hierarchical Dirichlet Process (HDP) prior for model learning, which is arguably best-suited for Markov process modeling. We then derive a context distillation procedure, which identifies and removes spurious contexts in an unsupervised fashion. We argue that the combination of these two components allows to infer the number of contexts from data thus dealing with the context cardinality assumption. We then find the representation of the optimal policy enabling efficient policy learning using off-the-shelf RL algorithms. Finally, we demonstrate empirically (using gym environments cart-pole swing-up, drone, intersection) that our approach succeeds where state-of-the-art methods of other frameworks fail and elaborate on the reasons for such failures.

We present a method for conditional sampling with normalizing flows when only part of an observation is available. We rely on the following fact: if the flow's domain can be partitioned in such a way that the flow restrictions to subdomains keep the bijectivity property, a lower bound to the conditioning variable log-probability can be derived. Simulation from the variational conditional flow then amends to solving an equality constraint. Our contribution is three-fold: a) we provide detailed insights on the choice of variational distributions; b) we propose how to partition the input space of the flow to preserve bijectivity property; c) we propose a set of methods to optimise the variational distribution in specific cases. Through extensive experiments, we show that our sampling method can be applied with success to invertible residual networks for inference and classification.

In this paper, we propose SAMBA, a novel framework for safe reinforcement learning that combines aspects from probabilistic modelling, information theory, and statistics. Our method builds upon PILCO to enable active exploration using novel(semi-)metrics for out-of-sample Gaussian process evaluation optimised through a multi-objective problem that supports conditional-value-at-risk constraints. We evaluate our algorithm on a variety of safe dynamical system benchmarks involving both low and high-dimensional state representations. Our results show orders of magnitude reductions in samples and violations compared to state-of-the-art methods. Lastly, we provide intuition as to the effectiveness of the framework by a detailed analysis of our active metrics and safety constraints.