Multi-task reinforcement learning (RL) aims to simultaneously learn policies for solving many tasks. Several prior works have found that relabeling past experience with different reward functions can improve sample efficiency. Relabeling methods typically ask: if, in hindsight, we assume that our experience was optimal for some task, for what task was it optimal? In this paper, we show that hindsight relabeling is inverse RL, an observation that suggests that we can use inverse RL in tandem for RL algorithms to efficiently solve many tasks. We use this idea to generalize goal-relabeling techniques from prior work to arbitrary classes of tasks. Our experiments confirm that relabeling data using inverse RL accelerates learning in general multi-task settings, including goal-reaching, domains with discrete sets of rewards, and those with linear reward functions.

Practitioners often rely on compute-intensive domain randomization to ensure reinforcement learning policies trained in simulation can robustly transfer to the real world. Due to unmodeled nonlinearities in the real system, however, even such simulated policies can still fail to perform stably enough to acquire experience in real environments. In this paper we propose a novel method that guarantees a stable region of attraction for the output of a policy trained in simulation, even for highly nonlinear systems. Our core technique is to use "bias-shifted" neural networks for constructing the controller and training the network in the simulator. The modified neural networks not only capture the nonlinearities of the system but also provably preserve linearity in a certain region of the state space and thus can be tuned to resemble a linear quadratic regulator that is known to be stable for the real system. We have tested our new method by transferring simulated policies for a swing-up inverted pendulum to real systems and demonstrated its efficacy.

We study the problem of how to efficiently explore zero-sum games whose payoffs and dynamics are initially unknown. The agent is given a certain number of episodes to learn as much useful information about the game as possible. During this learning, the rewards obtained in the game are fictional and thus do not count toward the evaluation of the final strategy. After this exploration phase, the agent must recommend a strategy that should be minimally exploitable by an adversary (who has complete knowledge of the environment and can thus play optimally against it). This setup is called pure exploration in the single-agent reinforcement learning literature. This is an important problem for simulation-based games in which a black-box simulator is queried with strategies to obtain samples of the players' resulting utilities [33], as opposed to the rules of the game being explicitly given. For example, in many military settings, war game simulators are used to generate strategies, and then the strategies need to be ready to deploy in case of actual war [17]. Another prevalent example is finance, where trading strategies are generated in simulation, and then they need to be ready for live trading. A third example is video games such as Dota 2 [4] and Starcraft II [31], where AIs can be trained largely through self-play.

In this paper, we propose a derivative-free model learning framework for Reinforcement Learning (RL) algorithms based on Gaussian Process Regression (GPR). In many mechanical systems, only positions can be measured by the sensing instruments. Then, instead of representing the system state as suggested by the physics with a collection of positions, velocities, and accelerations, we define the state as the set of past position measurements. However, the equation of motions derived by physical first principles cannot be directly applied in this framework, being functions of velocities and accelerations. For this reason, we introduce a novel derivative-free physically-inspired kernel, which can be easily combined with nonparametric derivative-free Gaussian Process models. Tests performed on two real platforms show that the considered state definition combined with the proposed model improves estimation performance and data-efficiency w.r.t. traditional models based on GPR. Finally, we validate the proposed framework by solving two RL control problems for two real robotic systems.

We consider the problem of finding Nash equilibrium for two-player turn-based zero-sum games. Inspired by the AlphaGo Zero (AGZ) algorithm, we develop a Reinforcement Learning based approach. Specifically, we propose Explore-Improve-Supervise (EIS) method that combines "exploration", "policy improvement"' and "supervised learning" to find the value function and policy associated with Nash equilibrium. We identify sufficient conditions for convergence and correctness for such an approach. For a concrete instance of EIS where random policy is used for "exploration", Monte-Carlo Tree Search is used for "policy improvement" and Nearest Neighbors is used for "supervised learning", we establish that this method finds an $\varepsilon$-approximate value function of Nash equilibrium in $\widetilde{O}(\varepsilon^{-(d+4)})$ steps when the underlying state-space of the game is continuous and $d$-dimensional. This is nearly optimal as we establish a lower bound of $\widetilde{\Omega}(\varepsilon^{-(d+2)})$ for any policy.

It has been a trend in the Reinforcement Learning literature to derive sample complexity bounds: a bound on how many experiences with the environment are required to obtain an $\varepsilon$-optimal policy. In the discounted cost, infinite horizon setting, all of the known bounds have a factor that is a polynomial in $1/(1-\beta)$, where $\beta < 1$ is the discount factor. For a large discount factor, these bounds seem to imply that a very large number of samples is required to achieve an $\varepsilon$-optimal policy. The objective of the present work is to introduce a new class of algorithms that have sample complexity uniformly bounded for all $\beta < 1$. One may argue that this is impossible, due to a recent min-max lower bound. The explanation is that this previous lower bound is for a specific problem, which we modify, without compromising the ultimate objective of obtaining an $\varepsilon$-optimal policy. Specifically, we show that the asymptotic variance of the Q-learning algorithm, with an optimized step-size sequence, is a quadratic function of $1/(1-\beta)$; an expected, and essentially known result. The new relative Q-learning algorithm proposed here is shown to have asymptotic variance that is a quadratic in $1/(1- \rho \beta)$, where $1 - \rho > 0$ is the spectral gap of an optimal transition matrix.

This paper studies the trajectory optimization problem for an aerial vehicle with the mission of flying between a pair of given initial and final locations. The objective is to minimize the travel time of the aerial vehicle ensuring that the communication connectivity constraint required for the safe operation of the aerial vehicle is satisfied. We consider two different criteria for the connectivity constraint of the aerial vehicle which leads to two different scenarios. In the first scenario, we assume that the maximum continuous time duration that the aerial vehicle is out of the coverage of the ground base stations (GBSs) is limited to a given threshold. In the second scenario, however, we assume that the total time periods that the aerial vehicle is not covered by the GBSs is restricted. Based on these two constraints, we formulate two trajectory optimization problems. To solve these non-convex problems, we use an approach based on the double Q-learning method which is a model-free reinforcement learning technique and unlike the existing algorithms does not need perfect knowledge of the environment. Moreover, in contrast to the well-known Q-learning technique, our double Q-learning algorithm does not suffer from the over-estimation issue. Simulation results show that although our algorithm does not require prior information of the environment, it works well and shows near optimal performance.

Emerging applications in robotics and autonomous systems, such as autonomous driving and robotic surgery, often involve critical safety constraints that must be satisfied even when information about system models is limited. In this regard, we propose a model-free safety specification method that learns the maximal probability of safe operation by carefully combining probabilistic reachability analysis and safe reinforcement learning (RL). Our approach constructs a Lyapunov function with respect to a safe policy to restrain each policy improvement stage. As a result, it yields a sequence of safe policies that determine the range of safe operation, called the safe set, which monotonically expands and gradually converges. We also develop an efficient safe exploration scheme that accelerates the process of identifying the safety of unexamined states. Exploiting the Lyapunov shielding, our method regulates the exploratory policy to avoid dangerous states with high confidence. To handle high-dimensional systems, we further extend our approach to deep RL by introducing a Lagrangian relaxation technique to establish a tractable actor-critic algorithm. The empirical performance of our method is demonstrated through continuous control benchmark problems, such as a reaching task on a planar robot arm.

In this paper, we consider the source of Deep Reinforcement Learning (DRL)'s sample complexity, asking how much derives from the requirement of learning useful representations of environment states and how much is due to the sample complexity of learning a policy. While for DRL agents, the distinction between representation and policy may not be clear, we seek new insight through a set of transfer learning experiments. In each experiment, we retain some fraction of layers trained on either the same game or a related game, comparing the benefits of transfer learning to learning a policy from scratch. Interestingly, we find that benefits due to transfer are highly variable in general and non-symmetric across pairs of tasks. Our experiments suggest that perhaps transfer from simpler environments can boost performance on more complex downstream tasks and that the requirements of learning a useful representation can range from negligible to the majority of the sample complexity, based on the environment. Furthermore, we find that fine-tuning generally outperforms training with the transferred layers frozen, confirming an insight first noted in the classification setting.

Mobile health (mHealth) interventions deliver treatments to users to support healthy behaviors. These interventions offer an opportunity for social impact in a diverse range of domains from substance abuse (Rabbi et al., 2017), to disease management (Hamine et al., 2015) to physical inactivity (Consolvo et al., 2008). For example, to help users increase their physical activity, an mHealth application might send a walking suggestions at times and in locations when a user is likely to be able to pursue the suggestions. The promise of mHealth hinges on the ability to provide interventions at times when users need the support and are receptive to it (Nahum-Shani et al., 2017). Consequently, in developing reinforcement learning (RL) algorithms for mHealth our goal is to be able to learn an optimal policy of when and how to intervene for a given user and context.