Policy Gradients with Variance Related Risk Criteria

Managing risk in dynamic decision problems is of cardinal importance in many fields such as finance and process control. The most common approach to defining risk is through various variance related criteria such as the Sharpe Ratio or the standard deviation adjusted reward. It is known that optimizing many of the variance related risk criteria is NP-hard. In this paper we devise a framework for local policy gradient style algorithms for reinforcement learning for variance related criteria. Our starting point is a new formula for the variance of the cost-to-go in episodic tasks. Using this formula we develop policy gradient algorithms for criteria that involve both the expected cost and the variance of the cost. We prove the convergence of these algorithms to local minima and demonstrate their applicability in a portfolio planning problem.Comment: Appears in Proceedings of the 29th International Conference on Machine Learning (ICML 2012

Practical Risk Measures in Reinforcement Learning

Practical application of Reinforcement Learning (RL) often involves risk considerations. We study a generalized approximation scheme for risk measures, based on Monte-Carlo simulations, where the risk measures need not necessarily be \emph{coherent}. We demonstrate that, even in simple problems, measures such as the variance of the reward-to-go do not capture the risk in a satisfactory manner. In addition, we show how a risk measure can be derived from model's realizations. We propose a neural architecture for estimating the risk and suggest the risk critic architecture that can be use to optimize a policy under general risk measures. We conclude our work with experiments that demonstrate the efficacy of our approach

Risk Averse Robust Adversarial Reinforcement Learning

Deep reinforcement learning has recently made significant progress in solving computer games and robotic control tasks. A known problem, though, is that policies overfit to the training environment and may not avoid rare, catastrophic events such as automotive accidents. A classical technique for improving the robustness of reinforcement learning algorithms is to train on a set of randomized environments, but this approach only guards against common situations. Recently, robust adversarial reinforcement learning (RARL) was developed, which allows efficient applications of random and systematic perturbations by a trained adversary. A limitation of RARL is that only the expected control objective is optimized; there is no explicit modeling or optimization of risk. Thus the agents do not consider the probability of catastrophic events (i.e., those inducing abnormally large negative reward), except through their effect on the expected objective. In this paper we introduce risk-averse robust adversarial reinforcement learning (RARARL), using a risk-averse protagonist and a risk-seeking adversary. We test our approach on a self-driving vehicle controller. We use an ensemble of policy networks to model risk as the variance of value functions. We show through experiments that a risk-averse agent is better equipped to handle a risk-seeking adversary, and experiences substantially fewer crashes compared to agents trained without an adversary.Comment: ICRA 201

Variance Adjusted Actor Critic Algorithms

We present an actor-critic framework for MDPs where the objective is the variance-adjusted expected return. Our critic uses linear function approximation, and we extend the concept of compatible features to the variance-adjusted setting. We present an episodic actor-critic algorithm and show that it converges almost surely to a locally optimal point of the objective function

Adaptive Symmetric Reward Noising for Reinforcement Learning

Recent reinforcement learning algorithms, though achieving impressive results in various fields, suffer from brittle training effects such as regression in results and high sensitivity to initialization and parameters. We claim that some of the brittleness stems from variance differences, i.e. when different environment areas - states and/or actions - have different rewards variance. This causes two problems: First, the "Boring Areas Trap" in algorithms such as Q-learning, where moving between areas depends on the current area variance, and getting out of a boring area is hard due to its low variance. Second, the "Manipulative Consultant" problem, when value-estimation functions used in DQN and Actor-Critic algorithms influence the agent to prefer boring areas, regardless of the mean rewards return, as they maximize estimation precision rather than rewards. This sheds a new light on how exploration contribute to training, as it helps with both challenges. Cognitive experiments in humans showed that noised reward signals may paradoxically improve performance. We explain this using the two mentioned problems, claiming that both humans and algorithms may share similar challenges. Inspired by this result, we propose the Adaptive Symmetric Reward Noising (ASRN), by which we mean adding Gaussian noise to rewards according to their states' estimated variance, thus avoiding the two problems while not affecting the environment's mean rewards behavior. We conduct our experiments in a Multi Armed Bandit problem with variance differences. We demonstrate that a Q-learning algorithm shows the brittleness effect in this problem, and that the ASRN scheme can dramatically improve the results. We show that ASRN helps a DQN algorithm training process reach better results in an end to end autonomous driving task using the AirSim driving simulator.Comment: 9 pages, 7 figures, conferenc

Multi-objective Model-based Policy Search for Data-efficient Learning with Sparse Rewards

The most data-efficient algorithms for reinforcement learning in robotics are model-based policy search algorithms, which alternate between learning a dynamical model of the robot and optimizing a policy to maximize the expected return given the model and its uncertainties. However, the current algorithms lack an effective exploration strategy to deal with sparse or misleading reward scenarios: if they do not experience any state with a positive reward during the initial random exploration, it is very unlikely to solve the problem. Here, we propose a novel model-based policy search algorithm, Multi-DEX, that leverages a learned dynamical model to efficiently explore the task space and solve tasks with sparse rewards in a few episodes. To achieve this, we frame the policy search problem as a multi-objective, model-based policy optimization problem with three objectives: (1) generate maximally novel state trajectories, (2) maximize the expected return and (3) keep the system in state-space regions for which the model is as accurate as possible. We then optimize these objectives using a Pareto-based multi-objective optimization algorithm. The experiments show that Multi-DEX is able to solve sparse reward scenarios (with a simulated robotic arm) in much lower interaction time than VIME, TRPO, GEP-PG, CMA-ES and Black-DROPS.Comment: Conference on Robot Learning (CoRL)- 2018; Code at https://github.com/resibots/kaushik_2018_multi-dex ; Video at https://youtu.be/9ZLwUxAAq6

Policy Evaluation with Variance Related Risk Criteria in Markov Decision Processes

In this paper we extend temporal difference policy evaluation algorithms to performance criteria that include the variance of the cumulative reward. Such criteria are useful for risk management, and are important in domains such as finance and process control. We propose both TD(0) and LSTD(lambda) variants with linear function approximation, prove their convergence, and demonstrate their utility in a 4-dimensional continuous state space problem

Decoupled Data Based Approach for Learning to Control Nonlinear Dynamical Systems

This paper addresses the problem of learning the optimal control policy for a nonlinear stochastic dynamical system with continuous state space, continuous action space and unknown dynamics. This class of problems are typically addressed in stochastic adaptive control and reinforcement learning literature using model-based and model-free approaches respectively. Both methods rely on solving a dynamic programming problem, either directly or indirectly, for finding the optimal closed loop control policy. The inherent `curse of dimensionality' associated with dynamic programming method makes these approaches also computationally difficult. This paper proposes a novel decoupled data-based control (D2C) algorithm that addresses this problem using a decoupled, `open loop - closed loop', approach. First, an open-loop deterministic trajectory optimization problem is solved using a black-box simulation model of the dynamical system. Then, a closed loop control is developed around this open loop trajectory by linearization of the dynamics about this nominal trajectory. By virtue of linearization, a linear quadratic regulator based algorithm can be used for this closed loop control. We show that the performance of D2C algorithm is approximately optimal. Moreover, simulation performance suggests significant reduction in training time compared to other state of the art algorithms

Emergent Complexity via Multi-Agent Competition

Reinforcement learning algorithms can train agents that solve problems in complex, interesting environments. Normally, the complexity of the trained agent is closely related to the complexity of the environment. This suggests that a highly capable agent requires a complex environment for training. In this paper, we point out that a competitive multi-agent environment trained with self-play can produce behaviors that are far more complex than the environment itself. We also point out that such environments come with a natural curriculum, because for any skill level, an environment full of agents of this level will have the right level of difficulty. This work introduces several competitive multi-agent environments where agents compete in a 3D world with simulated physics. The trained agents learn a wide variety of complex and interesting skills, even though the environment themselves are relatively simple. The skills include behaviors such as running, blocking, ducking, tackling, fooling opponents, kicking, and defending using both arms and legs. A highlight of the learned behaviors can be found here: https://goo.gl/eR7fbXComment: Published as a conference paper at ICLR 201

Reinforcement Learning

Reinforcement learning (RL) is a general framework for adaptive control, which has proven to be efficient in many domains, e.g., board games, video games or autonomous vehicles. In such problems, an agent faces a sequential decision-making problem where, at every time step, it observes its state, performs an action, receives a reward and moves to a new state. An RL agent learns by trial and error a good policy (or controller) based on observations and numeric reward feedback on the previously performed action. In this chapter, we present the basic framework of RL and recall the two main families of approaches that have been developed to learn a good policy. The first one, which is value-based, consists in estimating the value of an optimal policy, value from which a policy can be recovered, while the other, called policy search, directly works in a policy space. Actor-critic methods can be seen as a policy search technique where the policy value that is learned guides the policy improvement. Besides, we give an overview of some extensions of the standard RL framework, notably when risk-averse behavior needs to be taken into account or when rewards are not available or not known.Comment: Chapter in "A Guided Tour of Artificial Intelligence Research", Springe