Differentially Private Model-Based Offline Reinforcement Learning

We address offline reinforcement learning with privacy guarantees, where the goal is to train a policy that is differentially private with respect to individual trajectories in the dataset. To achieve this, we introduce DP-MORL, an MBRL algorithm coming with differential privacy guarantees. A private model of the environment is first learned from offline data using DP-FedAvg, a training method for neural networks that provides differential privacy guarantees at the trajectory level. Then, we use model-based policy optimization to derive a policy from the (penalized) private model, without any further interaction with the system or access to the input data. We empirically show that DP-MORL enables the training of private RL agents from offline data and we furthermore outline the price of privacy in this setting.

A Multi-step Loss Function for Robust Learning of the Dynamics in Model-based Reinforcement Learning

In model-based reinforcement learning, most algorithms rely on simulating trajectories from one-step models of the dynamics learned on data. A critical challenge of this approach is the compounding of one-step prediction errors as the length of the trajectory grows. In this paper we tackle this issue by using a multi-step objective to train one-step models. Our objective is a weighted sum of the mean squared error (MSE) loss at various future horizons. We find that this new loss is particularly useful when the data is noisy (additive Gaussian noise in the observations), which is often the case in real-life environments. To support the multi-step loss, first we study its properties in two tractable cases: i) uni-dimensional linear system, and ii) two-parameter non-linear system. Second, we show in a variety of tasks (environments or datasets) that the models learned with this loss achieve a significant improvement in terms of the averaged R2-score on future prediction horizons. Finally, in the pure batch reinforcement learning setting, we demonstrate that one-step models serve as strong baselines when dynamics are deterministic, while multi-step models would be more advantageous in the presence of noise, highlighting the potential of our approach in real-world applications.

Deep autoregressive density nets vs neural ensembles for model-based offline reinforcement learning

We consider the problem of offline reinforcement learning where only a set of system transitions is made available for policy optimization. Following recent advances in the field, we consider a model-based reinforcement learning algorithm that infers the system dynamics from the available data and performs policy optimization on imaginary model rollouts. This approach is vulnerable to exploiting model errors which can lead to catastrophic failures on the real system. The standard solution is to rely on ensembles for uncertainty heuristics and to avoid exploiting the model where it is too uncertain. We challenge the popular belief that we must resort to ensembles by showing that better performance can be obtained with a single well-calibrated autoregressive model on the D4RL benchmark. We also analyze static metrics of model-learning and conclude on the important model properties for the final performance of the agent.

Multi-timestep models for Model-based Reinforcement Learning

In model-based reinforcement learning (MBRL), most algorithms rely on simulating trajectories from one-step dynamics models learned on data. A critical challenge of this approach is the compounding of one-step prediction errors as length of the trajectory grows. In this paper we tackle this issue by using a multi-timestep objective to train one-step models. Our objective is a weighted sum of a loss function (e.g., negative log-likelihood) at various future horizons. We explore and test a range of weights profiles. We find that exponentially decaying weights lead to models that significantly improve the long-horizon R2 score. This improvement is particularly noticeable when the models were evaluated on noisy data. Finally, using a soft actor-critic (SAC) agent in pure batch reinforcement learning (RL) and iterated batch RL scenarios, we found that our multi-timestep models outperform or match standard one-step models. This was especially evident in a noisy variant of the considered environment, highlighting the potential of our approach in real-world applications.

Guided Safe Shooting: model based reinforcement learning with safety constraints

In the last decade, reinforcement learning successfully solved complex control tasks and decision-making problems, like the Go board game. Yet, there are few success stories when it comes to deploying those algorithms to real-world scenarios. One of the reasons is the lack of guarantees when dealing with and avoiding unsafe states, a fundamental requirement in critical control engineering systems. In this paper, we introduce Guided Safe Shooting (GuSS), a model-based RL approach that can learn to control systems with minimal violations of the safety constraints. The model is learned on the data collected during the operation of the system in an iterated batch fashion, and is then used to plan for the best action to perform at each time step. We propose three different safe planners, one based on a simple random shooting strategy and two based on MAP-Elites, a more advanced divergent-search algorithm. Experiments show that these planners help the learning agent avoid unsafe situations while maximally exploring the state space, a necessary aspect when learning an accurate model of the system. Furthermore, compared to model-free approaches, learning a model allows GuSS reducing the number of interactions with the real-system while still reaching high rewards, a fundamental requirement when handling engineering systems.

An $α$-No-Regret Algorithm For Graphical Bilinear Bandits

We propose the first regret-based approach to the Graphical Bilinear Bandits problem, where $n$ agents in a graph play a stochastic bilinear bandit game with each of their neighbors. This setting reveals a combinatorial NP-hard problem that prevents the use of any existing regret-based algorithm in the (bi-)linear bandit literature. In this paper, we fill this gap and present the first regret-based algorithm for graphical bilinear bandits using the principle of optimism in the face of uncertainty. Theoretical analysis of this new method yields an upper bound of $\tilde{O}(\sqrt{T})$ on the $\alpha$-regret and evidences the impact of the graph structure on the rate of convergence. Finally, we show through various experiments the validity of our approach.

Model-based micro-data reinforcement learning: what are the crucial model properties and which model to choose?

We contribute to micro-data model-based reinforcement learning (MBRL) by rigorously comparing popular generative models using a fixed (random shooting) control agent. We find that on an environment that requires multimodal posterior predictives, mixture density nets outperform all other models by a large margin. When multimodality is not required, our surprising finding is that we do not need probabilistic posterior predictives: deterministic models are on par, in fact they consistently (although non-significantly) outperform their probabilistic counterparts. We also found that heteroscedasticity at training time, perhaps acting as a regularizer, improves predictions at longer horizons. At the methodological side, we design metrics and an experimental protocol which can be used to evaluate the various models, predicting their asymptotic performance when using them on the control problem. Using this framework, we improve the state-of-the-art sample complexity of MBRL on Acrobot by two to four folds, using an aggressive training schedule which is outside of the hyperparameter interval usually considered

Refined bounds for randomized experimental design

Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a different criterion: mean square error, robustness, \emph{etc}. Computing such designs is generally an NP-hard problem and one can instead rely on a convex relaxation that considers probability distributions over the samples. Although greedy strategies and rounding procedures have received a lot of attention, straightforward sampling from the optimal distribution has hardly been investigated. In this paper, we propose theoretical guarantees for randomized strategies on E and G-optimal design. To this end, we develop a new concentration inequality for the eigenvalues of random matrices using a refined version of the intrinsic dimension that enables us to quantify the performance of such randomized strategies. Finally, we evidence the validity of our analysis through experiments, with particular attention on the G-optimal design applied to the best arm identification problem for linear bandits.

Best Arm Identification in Graphical Bilinear Bandits

We introduce a new graphical bilinear bandit problem where a learner (or a \emph{central entity}) allocates arms to the nodes of a graph and observes for each edge a noisy bilinear reward representing the interaction between the two end nodes. We study the best arm identification problem in which the learner wants to find the graph allocation maximizing the sum of the bilinear rewards. By efficiently exploiting the geometry of this bandit problem, we propose a somehow \emph{decentralized} allocation strategy based on random sampling with theoretical guarantees. In particular, we characterize the influence of the graph structure (e.g. star, complete or circle) on the convergence rate and propose empirical experiments that confirm this dependency.

Mass Volume Curves and Anomaly Ranking

This paper aims at formulating the issue of ranking multivariate unlabeled observations depending on their degree of abnormality as an unsupervised statistical learning task. In the 1-d situation, this problem is usually tackled by means of tail estimation techniques: univariate observations are viewed as all the more `abnormal' as they are located far in the tail(s) of the underlying probability distribution. It would be desirable as well to dispose of a scalar valued `scoring' function allowing for comparing the degree of abnormality of multivariate observations. Here we formulate the issue of scoring anomalies as a M-estimation problem by means of a novel functional performance criterion, referred to as the Mass Volume curve (MV curve in short), whose optimal elements are strictly increasing transforms of the density almost everywhere on the support of the density. We first study the statistical estimation of the MV curve of a given scoring function and we provide a strategy to build confidence regions using a smoothed bootstrap approach. Optimization of this functional criterion over the set of piecewise constant scoring functions is next tackled. This boils down to estimating a sequence of empirical minimum volume sets whose levels are chosen adaptively from the data, so as to adjust to the variations of the optimal MV curve, while controling the bias of its approximation by a stepwise curve. Generalization bounds are then established for the difference in sup norm between the MV curve of the empirical scoring function thus obtained and the optimal MV curve.