Smoothing Policies and Safe Policy Gradients

Policy gradient algorithms are among the best candidates for the much anticipated application of reinforcement learning to real-world control tasks, such as the ones arising in robotics. However, the trial-and-error nature of these methods introduces safety issues whenever the learning phase itself must be performed on a physical system. In this paper, we address a specific safety formulation, where danger is encoded in the reward signal and the learning agent is constrained to never worsen its performance. By studying actor-only policy gradient from a stochastic optimization perspective, we establish improvement guarantees for a wide class of parametric policies, generalizing existing results on Gaussian policies. This, together with novel upper bounds on the variance of policy gradient estimators, allows to identify those meta-parameter schedules that guarantee monotonic improvement with high probability. The two key meta-parameters are the step size of the parameter updates and the batch size of the gradient estimators. By a joint, adaptive selection of these meta-parameters, we obtain a safe policy gradient algorithm

Near Optimal Exploration-Exploitation in Non-Communicating Markov Decision Processes

While designing the state space of an MDP, it is common to include states that are transient or not reachable by any policy (e.g., in mountain car, the product space of speed and position contains configurations that are not physically reachable). This leads to defining weakly-communicating or multi-chain MDPs. In this paper, we introduce \tucrl, the first algorithm able to perform efficient exploration-exploitation in any finite Markov Decision Process (MDP) without requiring any form of prior knowledge. In particular, for any MDP with $S^{\texttt{C}}$ communicating states, $A$ actions and $\Gamma^{\texttt{C}} \leq S^{\texttt{C}}$ possible communicating next states, we derive a $\widetilde{O}(D^{\texttt{C}} \sqrt{\Gamma^{\texttt{C}} S^{\texttt{C}} AT})$ regret bound, where $D^{\texttt{C}}$ is the diameter (i.e., the longest shortest path) of the communicating part of the MDP. This is in contrast with optimistic algorithms (e.g., UCRL, Optimistic PSRL) that suffer linear regret in weakly-communicating MDPs, as well as posterior sampling or regularised algorithms (e.g., REGAL), which require prior knowledge on the bias span of the optimal policy to bias the exploration to achieve sub-linear regret. We also prove that in weakly-communicating MDPs, no algorithm can ever achieve a logarithmic growth of the regret without first suffering a linear regret for a number of steps that is exponential in the parameters of the MDP. Finally, we report numerical simulations supporting our theoretical findings and showing how TUCRL overcomes the limitations of the state-of-the-art

Inverse Reinforcement Learning through Policy Gradient Minimization

Inverse Reinforcement Learning (IRL) deals with the problem of recovering the reward function optimized by an expert given a set of demonstrations of the expert's policy.Most IRL algorithms need to repeatedly compute the optimal policy for different reward functions.This paper proposes a new IRL approach that allows to recover the reward function without the need of solving any "direct" RL problem.The idea is to find the reward function that minimizes the gradient of a parameterized representation of the expert's policy.In particular, when the reward function can be represented as a linear combination of some basis functions, we will show that the aforementioned optimization problem can be efficiently solved.We present an empirical evaluation of the proposed approach on a multidimensional version of the Linear-Quadratic Regulator (LQR) both in the case where the parameters of the expert's policy are known and in the (more realistic) case where the parameters of the expert's policy need to be inferred from the expert's demonstrations.Finally, the algorithm is compared against the state-of-the-art on the mountain car domain, where the expert's policy is unknown

Multi-objective reinforcement learning with continuous pareto frontier approximation

This paper is about learning a continuous approximation of the Pareto frontier in Multi-Objective Markov Decision Problems (MOMDPs). We propose a policy-based approach that exploits gradient information to generate solutions close to the Pareto ones. Differently from previous policy-gradient multi-objective algorithms, where n optimization routines are used to have n solutions, our approach performs a single gradient-ascent run that at each step generates an improved continuous approximation of the Pareto frontier. The idea is to exploit a gradient-based approach to optimize the parameters of a function that defines a manifold in the policy parameter space so that the corresponding image in the objective space gets as close as possible to the Pareto frontier. Besides deriving how to compute and estimate such gradient, we will also discuss the non-trivial issue of defining a metric to assess the quality of the candidate Pareto frontiers. Finally, the properties of the proposed approach are empirically evaluated on two interesting MOMDPs

Homomorphically Encrypted Linear Contextual Bandit

Contextual bandit is a general framework for online learning in sequential decision-making problems that has found application in a large range of domains, including recommendation system, online advertising, clinical trials and many more. A critical aspect of bandit methods is that they require to observe the contexts -- i.e., individual or group-level data -- and the rewards in order to solve the sequential problem. The large deployment in industrial applications has increased interest in methods that preserve the privacy of the users. In this paper, we introduce a privacy-preserving bandit framework based on asymmetric encryption. The bandit algorithm only observes encrypted information (contexts and rewards) and has no ability to decrypt it. Leveraging homomorphic encryption, we show that despite the complexity of the setting, it is possible to learn over encrypted data. We introduce an algorithm that achieves a $\widetilde{O}(d\sqrt{T})$ regret bound in any linear contextual bandit problem, while keeping data encrypted