Model-free reinforcement learning (RL) provides an attractive approach for learning control policies directly in high dimensional state spaces. However, many goal-oriented tasks involving sparse rewards remain difficult to solve with state-of-the-art model-free RL algorithms, even in simulation. One of the key difficulties is that deep RL, due to its relatively poor sample complexity, often requires a prohibitive number of trials to obtain a learning signal. We propose a novel, non-sparse reward function for robotic RL tasks by leveraging physical priors in the form of a time-to-reach (TTR) function computed from an approximate system dynamics model. TTR functions come from the optimal control field and measure the minimal time required to move from any state to the goal. However, TTR functions are intractable to compute for complex systems, so we compute it in a lower-dimensional state space, and then do a simple transformation to convert it into a TTR-based reward function for the MDP in RL tasks. Our TTR-based reward function provides highly-informative rewards that account for system dynamics.
This paper presents a new approach to hierarchical reinforcement learning based on the MAXQ decomposition of the value function. The MAXQ decomposition has both a procedural semantics—as a subroutine hierarchy—and a declarative semantics—as a representation of the value function of a hierarchical policy. MAXQ unifies and extends previous work on hierarchical reinforcement learning by Singh, Kaelbling, and Dayan and Hinton. Conditions under which the MAXQ decomposition can represent the optimal value function are derived. The paper defines a hierarchical Q learning algorithm, proves its convergence, and shows experimentally that it can learn much faster than ordinary “flat” Q learning. Finally, the paper discusses some interesting issues that arise in hierarchical reinforcement learning including the hierarchical credit assignment problem and non-hierarchical execution of the MAXQ hierarchy. Learning, planning, and representing knowledge at multiple levels of temporal ab- straction are key, longstanding challenges for AI. In this paper we consider how these challenges can be addressed within the mathematical framework of reinforce- ment learning and Markov decision processes (MDPs). We extend the usual notion of action in this framework to include options—closed-loop policies for taking ac- tion over a period of time. Examples of options include picking up an object, going to lunch, and traveling to a distant city, as well as primitive actions such as mus- cle twitches and joint torques. Overall, we show that options enable temporally abstract knowledge and action to be included in the reinforcement learning frame- work in a natural and general way. In particular, we show that options may be used interchangeably with primitive actions in planning methods such as dynamic pro- gramming and in learning methods such as Q-learning. Formally, a set of options defined over an MDP constitutes a semi-Markov decision process (SMDP), and the theory of SMDPs provides the foundation for the theory of options. However, the most interesting issues concern the interplay between the underlying MDP and the SMDP and are thus beyond SMDP theory. We present results for three such cases: 1) we show that the results of planning with options can be used during execution to interrupt options and thereby perform even better than planned, 2) we introduce new intra-option methods that are able to learn about an option from fragments of its execution, and 3) we propose a notion of subgoal that can be used to improve the options themselves. All of these results have precursors in the existing literature; the contribution of this paper is to establish them in a simpler and more general setting with fewer changes to the existing reinforcement learning framework. In particular, we show that these results can be obtained without committing to (or ruling out) any particular approach to state abstraction, hierarchy, function approximation, or the macro-utility problem. Efficient exploration remains a major challenge for reinforcement learning (RL). Common dithering strategies for exploration, such as '-greedy, do not carry out temporally-extended (or deep) exploration; this can lead to exponentially larger data requirements. However, most algorithms for statistically efficient RL are not computationally tractable in complex environments. Randomized value functions offer a promising approach to efficient exploration with generalization, but existing algorithms are not compatible with nonlinearly parameterized value functions. As a first step towards addressing such contexts we develop bootstrapped DQN. We demonstrate that bootstrapped DQN can combine deep exploration with deep neural networks for exponentially faster learning than any dithering strategy. In the Arcade Learning Environment bootstrapped DQN substantially improves learning speed and cumulative performance across most games. Learning goal-directed behavior in environments with sparse feedback is a major challenge for reinforcement learning algorithms. One of the key difficulties is insufficient exploration, resulting in an agent being unable to learn robust policies. Intrinsically motivated agents can explore new behavior for their own sake rather than to directly solve external goals. Such intrinsic behaviors could eventually help the agent solve tasks posed by the environment. We present hierarchical-DQN (h-DQN), a framework to integrate hierarchical action-value functions, operating at different temporal scales, with goal-driven intrinsically motivated deep reinforcement learning. A top-level q-value function learns a policy over intrinsic goals, while a lower-level function learns a policy over atomic actions to satisfy the given goals. h-DQN allows for flexible goal specifications, such as functions over entities and relations. This provides an efficient space for exploration in complicated environments. We demonstrate the strength of our approach on two problems with very sparse and delayed feedback: (1) a complex discrete stochastic decision process with stochastic transitions, and (2) the classic ATARI game -'Montezuma's Revenge'. 