Value Iteration in Continuous Actions, States and Time

Classical value iteration approaches are not applicable to environments with continuous states and actions. For such environments, the states and actions are usually discretized, which leads to an exponential increase in computational complexity. In this paper, we propose continuous fitted value iteration (cFVI). This algorithm enables dynamic programming for continuous states and actions with a known dynamics model. Leveraging the continuous-time formulation, the optimal policy can be derived for non-linear control-affine dynamics. This closed-form solution enables the efficient extension of value iteration to continuous environments. We show in non-linear control experiments that the dynamic programming solution obtains the same quantitative performance as deep reinforcement learning methods in simulation but excels when transferred to the physical system. The policy obtained by cFVI is more robust to changes in the dynamics despite using only a deterministic model and without explicitly incorporating robustness in the optimization. Videos of the physical system are available at \url{https://sites.google.com/view/value-iteration}.

Noise Estimation Is Not Optimal: How To Use Kalman Filter The Right Way

Determining the noise parameters of a Kalman Filter (KF) has been researched for decades. The research focuses on the task of estimation of the noise under various conditions, since precise noise estimation is considered equivalent to errors minimization. However, we show that even a small violation of KF assumptions can significantly modify the effective noise, breaking the equivalence between the tasks and making noise estimation an inferior strategy. We show that such violations are very common, and are often not trivial to handle or even notice. Consequentially, we argue that a robust solution is needed - rather than choosing a dedicated model per problem. To that end, we use a simple parameterization to apply gradient-based optimization efficiently to the symmetric and positive-definite parameters of KF. In radar tracking and video tracking, we show that the optimization improves both the accuracy of KF and its robustness to design decisions. In addition, we demonstrate how a neural network model can seem to reduce the errors significantly compared to a KF - and how this reduction vanishes once the KF is optimized. This indicates how complicated models can be wrongly identified as superior to KF, while in fact they were merely over-optimized.

Better than the Best: Gradient-based Improper Reinforcement Learning for Network Scheduling

We consider the problem of scheduling in constrained queueing networks with a view to minimizing packet delay. Modern communication systems are becoming increasingly complex, and are required to handle multiple types of traffic with widely varying characteristics such as arrival rates and service times. This, coupled with the need for rapid network deployment, render a bottom up approach of first characterizing the traffic and then devising an appropriate scheduling protocol infeasible. In contrast, we formulate a top down approach to scheduling where, given an unknown network and a set of scheduling policies, we use a policy gradient based reinforcement learning algorithm that produces a scheduler that performs better than the available atomic policies. We derive convergence results and analyze finite time performance of the algorithm. Simulation results show that the algorithm performs well even when the arrival rates are nonstationary and can stabilize the system even when the constituent policies are unstable.

Using Kalman Filter The Right Way: Noise Estimation Is Not Optimal

Determining the noise parameters of a Kalman Filter (KF) has been researched for decades. The research focuses on estimation of the noise under various conditions, since noise estimation is considered equivalent to errors minimization. However, we show that even a seemingly small violation of KF assumptions can significantly modify the effective noise, breaking the equivalence between the tasks and making noise estimation a highly sub-optimal strategy. In particular, whoever tests a new learning-based algorithm in comparison to a (variant of) KF with standard parameters tuning, essentially conducts an unfair comparison between an optimized algorithm and a non-optimized one. We suggest a method (based on Cholesky decomposition) to apply gradient-based optimization efficiently to the symmetric and positive-definite (SPD) parameters of KF, so that KF can be optimized similarly to common neural networks. The benefits of this method are demonstrated for both Radar tracking and video tracking. For Radar tracking we also show how a non-linear neural-network-based model can seem to reduce the tracking errors significantly compared to a KF - and how this reduction entirely vanishes once the KF is optimized. Through a detailed case-study, we also demonstrate that KF requires non-trivial design-decisions to be made, and that parameters optimization makes KF more robust to these decisions.

Maximum Entropy Reinforcement Learning with Mixture Policies

Mixture models are an expressive hypothesis class that can approximate a rich set of policies. However, using mixture policies in the Maximum Entropy (MaxEnt) framework is not straightforward. The entropy of a mixture model is not equal to the sum of its components, nor does it have a closed-form expression in most cases. Using such policies in MaxEnt algorithms, therefore, requires constructing a tractable approximation of the mixture entropy. In this paper, we derive a simple, low-variance mixture-entropy estimator. We show that it is closely related to the sum of marginal entropies. Equipped with our entropy estimator, we derive an algorithmic variant of Soft Actor-Critic (SAC) to the mixture policy case and evaluate it on a series of continuous control tasks.

Action Redundancy in Reinforcement Learning

Maximum Entropy (MaxEnt) reinforcement learning is a powerful learning paradigm which seeks to maximize return under entropy regularization. However, action entropy does not necessarily coincide with state entropy, e.g., when multiple actions produce the same transition. Instead, we propose to maximize the transition entropy, i.e., the entropy of next states. We show that transition entropy can be described by two terms; namely, model-dependent transition entropy and action redundancy. Particularly, we explore the latter in both deterministic and stochastic settings and develop tractable approximation methods in a near model-free setup. We construct algorithms to minimize action redundancy and demonstrate their effectiveness on a synthetic environment with multiple redundant actions as well as contemporary benchmarks in Atari and Mujoco. Our results suggest that action redundancy is a fundamental problem in reinforcement learning.

GELATO: Geometrically Enriched Latent Model for Offline Reinforcement Learning

Offline reinforcement learning approaches can generally be divided to proximal and uncertainty-aware methods. In this work, we demonstrate the benefit of combining the two in a latent variational model. We impose a latent representation of states and actions and leverage its intrinsic Riemannian geometry to measure distance of latent samples to the data. Our proposed metrics measure both the quality of out of distribution samples as well as the discrepancy of examples in the data. We integrate our metrics in a model-based offline optimization framework, in which proximity and uncertainty can be carefully controlled. We illustrate the geodesics on a simple grid-like environment, depicting its natural inherent topology. Finally, we analyze our approach and improve upon contemporary offline RL benchmarks.

Improper Learning with Gradient-based Policy Optimization

We consider an improper reinforcement learning setting where the learner is given M base controllers for an unknown Markov Decision Process, and wishes to combine them optimally to produce a potentially new controller that can outperform each of the base ones. We propose a gradient-based approach that operates over a class of improper mixtures of the controllers. The value function of the mixture and its gradient may not be available in closed-form; however, we show that we can employ rollouts and simultaneous perturbation stochastic approximation (SPSA) for explicit gradient descent optimization. We derive convergence and convergence rate guarantees for the approach assuming access to a gradient oracle. Numerical results on a challenging constrained queueing task show that our improper policy optimization algorithm can stabilize the system even when each constituent policy at its disposal is unstable.

Reinforcement Learning for Datacenter Congestion Control

We approach the task of network congestion control in datacenters using Reinforcement Learning (RL). Successful congestion control algorithms can dramatically improve latency and overall network throughput. Until today, no such learning-based algorithms have shown practical potential in this domain. Evidently, the most popular recent deployments rely on rule-based heuristics that are tested on a predetermined set of benchmarks. Consequently, these heuristics do not generalize well to newly-seen scenarios. Contrarily, we devise an RL-based algorithm with the aim of generalizing to different configurations of real-world datacenter networks. We overcome challenges such as partial-observability, non-stationarity, and multi-objectiveness. We further propose a policy gradient algorithm that leverages the analytical structure of the reward function to approximate its derivative and improve stability. We show that this scheme outperforms alternative popular RL approaches, and generalizes to scenarios that were not seen during training. Our experiments, conducted on a realistic simulator that emulates communication networks' behavior, exhibit improved performance concurrently on the multiple considered metrics compared to the popular algorithms deployed today in real datacenters. Our algorithm is being productized to replace heuristics in some of the largest datacenters in the world.