Papers

The use of deep neural networks as function approximators has led to striking progress for reinforcement learning algorithms and applications. Yet the knowledge we have on decision boundary geometry and the loss landscape of neural policies is still quite limited. In this paper we propose a framework to investigate the decision boundary and loss landscape similarities across states and across MDPs. We conduct experiments in various games from Arcade Learning Environment, and discover that high sensitivity directions for neural policies are correlated across MDPs. We argue that these high sensitivity directions support the hypothesis that non-robust features are shared across training environments of reinforcement learning agents. We believe our results reveal fundamental properties of the environments used in deep reinforcement learning training, and represent a tangible step towards building robust and reliable deep reinforcement learning agents.

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This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based methods, the proposed architecture generates a latent variable in each data block with a length of multiple timesteps and passes the most relevant information to the next block for policy optimization. The proposed blockwise sequential model is implemented based on self-attention, making the model capable of detailed sequential learning in partial observable settings. The proposed model builds an additional learning network to efficiently implement gradient estimation by using self-normalized importance sampling, which does not require the complex blockwise input data reconstruction in the model learning. Numerical results show that the proposed method significantly outperforms previous methods in various partially observable environments.

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Learning in a lifelong setting, where the dynamics continually evolve, is a hard challenge for current reinforcement learning algorithms. Yet this would be a much needed feature for practical applications. In this paper, we propose an approach which learns a hyper-policy, whose input is time, that outputs the parameters of the policy to be queried at that time. This hyper-policy is trained to maximize the estimated future performance, efficiently reusing past data by means of importance sampling, at the cost of introducing a controlled bias. We combine the future performance estimate with the past performance to mitigate catastrophic forgetting. To avoid overfitting the collected data, we derive a differentiable variance bound that we embed as a penalization term. Finally, we empirically validate our approach, in comparison with state-of-the-art algorithms, on realistic environments, including water resource management and trading.

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Cooperative multi-agent reinforcement learning (MARL) faces significant scalability issues due to state and action spaces that are exponentially large in the number of agents. As environments grow in size, effective credit assignment becomes increasingly harder and often results in infeasible learning times. Still, in many real-world settings, there exist simplified underlying dynamics that can be leveraged for more scalable solutions. In this work, we exploit such locality structures effectively whilst maintaining global cooperation. We propose a novel, value-based multi-agent algorithm called LOMA$Q$, which incorporates local rewards in the Centralized Training Decentralized Execution paradigm. Additionally, we provide a direct reward decomposition method for finding these local rewards when only a global signal is provided. We test our method empirically, showing it scales well compared to other methods, significantly improving performance and convergence speed.

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In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common approximation, which has been recently popularized as meta-RL, is to train the agent on a sample of N problem instances from the prior, with the hope that for large enough N, good generalization behavior to an unseen test instance will be obtained. In this work, we study generalization in Bayesian RL under the probably approximately correct (PAC) framework, using the method of algorithmic stability. Our main contribution is showing that by adding regularization, the optimal policy becomes uniformly stable in an appropriate sense. Most stability results in the literature build on strong convexity of the regularized loss -- an approach that is not suitable for RL as Markov decision processes (MDPs) are not convex. Instead, building on recent results of fast convergence rates for mirror descent in regularized MDPs, we show that regularized MDPs satisfy a certain quadratic growth criterion, which is sufficient to establish stability. This result, which may be of independent interest, allows us to study the effect of regularization on generalization in the Bayesian RL setting.

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Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches. First, physics-informed neural networks (PINNs) learn continuous solutions of PDEs and can be trained with little to no ground truth data. However, PINNs do not generalize well to unseen domains. Second, convolutional neural networks provide fast inference and generalize but either require large amounts of training data or a physics-constrained loss based on finite differences that can lead to inaccuracies and discretization artifacts. We leverage the advantages of both of these approaches by using Hermite spline kernels in order to continuously interpolate a grid-based state representation that can be handled by a CNN. This allows for training without any precomputed training data using a physics-informed loss function only and provides fast, continuous solutions that generalize to unseen domains. We demonstrate the potential of our method at the examples of the incompressible Navier-Stokes equation and the damped wave equation. Our models are able to learn several intriguing phenomena such as Karman vortex streets, the Magnus effect, Doppler effect, interference patterns and wave reflections. Our quantitative assessment and an interactive real-time demo show that we are narrowing the gap in accuracy of unsupervised ML based methods to industrial solvers for computational fluid dynamics (CFD) while being orders of magnitude faster.

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Good representations can help RL agents perform concise modeling of their surroundings, and thus support effective decision-making in complex environments. Previous methods learn good representations by imposing extra constraints on dynamics. However, in the causal perspective, the causation between the action and its effect is not fully considered in those methods, which leads to the ignorance of the underlying relations among the action effects on the transitions. Based on the intuition that the same action always causes similar effects among different states, we induce such causation by taking the invariance of action effects among states as the relation. By explicitly utilizing such invariance, in this paper, we show that a better representation can be learned and potentially improves the sample efficiency and the generalization ability of the learned policy. We propose \textbf{I}nvariant \textbf{A}ction \textbf{E}ffect \textbf{M}odel (IAEM) to capture the invariance in action effects, where the effect of an action is represented as the residual of representations from neighboring states. IAEM is composed of two parts: (1) a new contrastive-based loss to capture the underlying invariance of action effects; (2) an individual action effect and provides a self-adapted weighting strategy to tackle the corner cases where the invariance does not hold. The extensive experiments on two benchmarks, i.e. Grid-World and Atari, show that the representations learned by IAEM preserve the invariance of action effects. Moreover, with the invariant action effect, IAEM can accelerate the learning process by 1.6x, rapidly generalize to new environments by fine-tuning on a few components, and outperform other dynamics-based representation methods by 1.4x in limited steps.

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Reward-Weighted Regression (RWR) belongs to a family of widely known iterative Reinforcement Learning algorithms based on the Expectation-Maximization framework. In this family, learning at each iteration consists of sampling a batch of trajectories using the current policy and fitting a new policy to maximize a return-weighted log-likelihood of actions. Although RWR is known to yield monotonic improvement of the policy under certain circumstances, whether and under which conditions RWR converges to the optimal policy have remained open questions. In this paper, we provide for the first time a proof that RWR converges to a global optimum when no function approximation is used, in a general compact setting. Furthermore, for the simpler case with finite state and action spaces we prove R-linear convergence of the state-value function to the optimum.

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To accumulate knowledge and improve its policy of behaviour, a reinforcement learning agent can learn `off-policy' about policies that differ from the policy used to generate its experience. This is important to learn counterfactuals, or because the experience was generated out of its own control. However, off-policy learning is non-trivial, and standard reinforcement-learning algorithms can be unstable and divergent. In this paper we discuss a novel family of off-policy prediction algorithms which are convergent by construction. The idea is to first learn on-policy about the data-generating behaviour, and then bootstrap an off-policy value estimate on this on-policy estimate, thereby constructing a value estimate that is partially off-policy. This process can be repeated to build a chain of value functions, each time bootstrapping a new estimate on the previous estimate in the chain. Each step in the chain is stable and hence the complete algorithm is guaranteed to be stable. Under mild conditions this comes arbitrarily close to the off-policy TD solution when we increase the length of the chain. Hence it can compute the solution even in cases where off-policy TD diverges. We prove that the proposed scheme corresponds to an iterative decomposition of the inverse key matrix. Empirically we evaluate the idea on challenging MDPs such as Baird's counter example and observe favourable results.

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Deep reinforcement learning algorithms can perform poorly in real-world tasks due to the discrepancy between source and target environments. This discrepancy is commonly viewed as the disturbance in transition dynamics. Many existing algorithms learn robust policies by modeling the disturbance and applying it to source environments during training, which usually requires prior knowledge about the disturbance and control of simulators. However, these algorithms can fail in scenarios where the disturbance from target environments is unknown or is intractable to model in simulators. To tackle this problem, we propose a novel model-free actor-critic algorithm---namely, state-conservative policy optimization (SCPO)---to learn robust policies without modeling the disturbance in advance. Specifically, SCPO reduces the disturbance in transition dynamics to that in state space and then approximates it by a simple gradient-based regularizer. The appealing features of SCPO include that it is simple to implement and does not require additional knowledge about the disturbance or specially designed simulators. Experiments in several robot control tasks demonstrate that SCPO learns robust policies against the disturbance in transition dynamics.

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Several recent works have been dedicated to unsupervised reinforcement learning in a single environment, in which a policy is first pre-trained with unsupervised interactions, and then fine-tuned towards the optimal policy for several downstream supervised tasks defined over the same environment. Along this line, we address the problem of unsupervised reinforcement learning in a class of multiple environments, in which the policy is pre-trained with interactions from the whole class, and then fine-tuned for several tasks in any environment of the class. Notably, the problem is inherently multi-objective as we can trade off the pre-training objective between environments in many ways. In this work, we foster an exploration strategy that is sensitive to the most adverse cases within the class. Hence, we cast the exploration problem as the maximization of the mean of a critical percentile of the state visitation entropy induced by the exploration strategy over the class of environments. Then, we present a policy gradient algorithm, $\alpha$MEPOL, to optimize the introduced objective through mediated interactions with the class. Finally, we empirically demonstrate the ability of the algorithm in learning to explore challenging classes of continuous environments and we show that reinforcement learning greatly benefits from the pre-trained exploration strategy w.r.t. learning from scratch.

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Basketball is one of the most popular types of sports in the world. Recent technological developments have made it possible to collect large amounts of data on the game, analyze it, and discover new insights. We propose a novel approach for modeling basketball games using deep reinforcement learning. By analyzing multiple aspects of both the players and the game, we are able to model the latent connections among players' movements, actions, and performance, into a single measure - the Q-Ball. Using Q-Ball, we are able to assign scores to the performance of both players and whole teams. Our approach has multiple practical applications, including evaluating and improving players' game decisions and producing tactical recommendations. We train and evaluate our approach on a large dataset of National Basketball Association games, and show that the Q-Ball is capable of accurately assessing the performance of players and teams. Furthermore, we show that Q-Ball is highly effective in recommending alternatives to players' actions.

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In this work we continue to build upon recent advances in reinforcement learning for finite Markov processes. A common approach among previous existing algorithms, both single-actor and distributed, is to either clip rewards or to apply a transformation method on Q-functions to handle a large variety of magnitudes in real discounted returns. We theoretically show that one of the most successful methods may not yield an optimal policy if we have a non-deterministic process. As a solution, we argue that distributional reinforcement learning lends itself to remedy this situation completely. By the introduction of a conjugate distributional operator, we may handle a large class of transformations for real returns with guaranteed theoretical convergence. We propose an approximating single-actor algorithm based on this operator that trains agents directly on raw rewards using a proper distributional metric given by the Cramér distance. To evaluate its performance in a stochastic setting we train agents on a suite of 55 Atari 2600 games using sticky-actions and obtain state-of-the-art performance compared to other well-known algorithms in the Dopamine framework.

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The human intrinsic desire to pursue knowledge, also known as curiosity, is considered essential in the process of skill acquisition. With the aid of artificial curiosity, we could equip current techniques for control, such as Reinforcement Learning, with more natural exploration capabilities. A promising approach in this respect has consisted of using Bayesian surprise on model parameters, i.e. a metric for the difference between prior and posterior beliefs, to favour exploration. In this contribution, we propose to apply Bayesian surprise in a latent space representing the agent’s current understanding of the dynamics of the system, drastically reducing the computational costs. We extensively evaluate our method by measuring the agent's performance in terms of environment exploration, for continuous tasks, and looking at the game scores achieved, for video games. Our model is computationally cheap and compares positively with current state-of-the-art methods on several problems. We also investigate the effects caused by stochasticity in the environment, which is often a failure case for curiosity-driven agents. In this regime, the results suggest that our approach is resilient to stochastic transitions.

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We study a finite-horizon restless multi-armed bandit problem with multiple actions, dubbed as R(MA)^2B. The state of each arm evolves according to a controlled Markov decision process (MDP), and the reward of pulling an arm depends on both the current state and action of the corresponding MDP. Since finding the optimal policy is typically intractable, we propose a computationally appealing index policy entitled Occupancy-Measured-Reward Index Policy for the finite-horizon R(MA)^2B. Our index policy is well-defined without the requirement of indexability condition and is provably asymptotically optimal as the number of arms tends to infinity. We then adopt a learning perspective where the system parameters are unknown, and propose R(MA)^2B-UCB, a generative model based reinforcement learning augmented algorithm that can fully exploit the structure of Occupancy-Measured-Reward Index Policy. Compared to existing algorithms, R(MA)^2B-UCB performs close to offline optimum, and achieves a sub-linear regret and a low computational complexity all at once. Experimental results show that R(MA)^2B-UCB outperforms existing algorithms in both regret and running time.

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We consider Reinforcement Learning (RL) problems where an agent attempts to maximize a reward signal while minimizing a cost function that models unsafe behaviors. Such formalization is addressed in the literature using constrained optimization on the cost, limiting the exploration and leading to a significant trade-off between cost and reward. In contrast, we propose a Safety-Oriented Search that complements Deep RL algorithms to bias the policy toward safety within an evolutionary cost optimization. We leverage evolutionary exploration benefits to design a novel concept of safe mutations that use visited unsafe states to explore safer actions. We further characterize the behaviors of the policies over desired specifics with a sample-based bound estimation, which makes prior verification analysis tractable in the training loop. Hence, driving the learning process towards safer regions of the policy space. Empirical evidence on the Safety Gym benchmark shows that we successfully avoid drawbacks on the return while improving the safety of the policy.

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Despite of achieving great success in real life, Deep Reinforcement Learning (DRL) is still suffering from three critical issues, which are data efficiency, lack of the interpretability and transferability. Recent research shows that embedding symbolic knowledge into DRL is promising in addressing those challenges. Inspired by this, we introduce a novel deep reinforcement learning framework with symbolic options. This framework features a loop training procedure, which enables guiding the improvement of policy by planning with action models and symbolic options learned from interactive trajectories automatically. The learned symbolic options help doing the dense requirement of expert domain knowledge and provide inherent interpretabiliy of policies. Moreover, the transferability and data efficiency can be further improved by planning with the action models. To validate the effectiveness of this framework, we conduct experiments on two domains, Montezuma's Revenge and Office World respectively, and the results demonstrate the comparable performance, improved data efficiency, interpretability and transferability.

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Sample efficiency is crucial for imitation learning methods to be applicable in real-world applications. Many studies improve sample efficiency by extending adversarial imitation to be off-policy regardless of the fact that these off-policy extensions could either change the original objective or involve complicated optimization. We revisit the foundation of adversarial imitation and propose an off-policy sample efficient approach that requires no adversarial training or min-max optimization. Our formulation capitalizes on two key insights: (1) the similarity between the Bellman equation and the stationary state-action distribution equation allows us to derive a novel temporal difference (TD) learning approach; and (2) the use of a deterministic policy simplifies the TD learning. Combined, these insights yield a practical algorithm, Deterministic and Discriminative Imitation (D2-Imitation), which oper- ates by first partitioning samples into two replay buffers and then learning a deterministic policy via off-policy reinforcement learning. Our empirical results show that D2-Imitation is effective in achieving good sample efficiency, outperforming several off-policy extension approaches of adversarial imitation on many control tasks.

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In Apprenticeship Learning (AL), we are given a Markov Decision Process (MDP) without access to the cost function. Instead, we observe trajectories sampled by an expert that acts according to some policy. The goal is to find a policy that matches the expert's performance on some predefined set of cost functions. We introduce an online variant of AL (Online Apprenticeship Learning; OAL), where the agent is expected to perform comparably to the expert while interacting with the environment. We show that the OAL problem can be effectively solved by combining two mirror descent based no-regret algorithms: one for policy optimization and another for learning the worst case cost. By employing optimistic exploration, we derive a convergent algorithm with $O(\sqrt{K})$ regret, where $K$ is the number of interactions with the MDP, and an additional linear error term that depends on the amount of expert trajectories available. Importantly, our algorithm avoids the need to solve an MDP at each iteration, making it more practical compared to prior AL methods. Finally, we implement a deep variant of our algorithm which shares some similarities to GAIL \cite{ho2016generative}, but where the discriminator is replaced with the costs learned by the OAL problem. Our simulations suggest that OAL performs well in high dimensional control problems.

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Multi-agent reinforcement learning (MARL) provides an efficient way for simultaneously learning policies for multiple agents interacting with each other. However, in scenarios requiring complex interactions, existing algorithms can suffer from an inability to accurately anticipate the influence of self-actions on other agents. Incorporating an ability to reason about other agents' potential responses can allow an agent to formulate more effective strategies. This paper adopts a recursive reasoning model in a centralized-training-decentralized-execution framework to help learning agents better cooperate with or compete against others. The proposed algorithm, referred to as the Recursive Reasoning Graph (R2G), shows state-of-the-art performance on multiple multi-agent particle and robotics games.

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Model-based reinforcement learning algorithms, which aim to learn a model of the environment to make decisions, are more sample efficient than their model-free counterparts. The sample efficiency of model-based approaches relies on whether the model can well approximate the environment. However, learning an accurate model is challenging, especially in complex and noisy environments. To tackle this problem, we propose the conservative model-based actor-critic (CMBAC), a novel approach that achieves high sample efficiency without the strong reliance on accurate learned models. Specifically, CMBAC learns multiple estimates of the Q-value function from a set of inaccurate models and uses the average of the bottom-k estimates---a conservative estimate---to optimize the policy. An appealing feature of CMBAC is that the conservative estimates effectively encourage the agent to avoid unreliable “promising actions”---whose values are high in only a small fraction of the models. Experiments demonstrate that CMBAC significantly outperforms state-of-the-art approaches in terms of sample efficiency on several challenging control tasks, and the proposed method is more robust than previous methods in noisy environments.

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An artificial neural network can be trained by uniformly broadcasting a reward signal to units that implement a REINFORCE learning rule. Though this presents a biologically plausible alternative to backpropagation in training a network, the high variance associated with it renders it impractical to train deep networks. The high variance arises from the inefficient structural credit assignment since a single reward signal is used to evaluate the collective action of all units. To facilitate structural credit assignment, we propose replacing the reward signal to hidden units with the change in the $L^2$ norm of the unit's outgoing weight. As such, each hidden unit in the network is trying to maximize the norm of its outgoing weight instead of the global reward, and thus we call this learning method \emph{Weight Maximization}. We prove that Weight Maximization is approximately following the gradient of rewards in expectation. In contrast to backpropagation, Weight Maximization can be used to train both continuous-valued and discrete-valued units. Moreover, Weight Maximization solves several major issues of backpropagation relating to biological plausibility. Our experiments show that a network trained with Weight Maximization can learn significantly faster than REINFORCE and slightly slower than backpropagation. Weight Maximization illustrates an example of cooperative behavior automatically arising from a population of self-interested agents in a competitive game without any central coordination.

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We study Policy-extended Value Function Approximator (PeVFA) in Reinforcement Learning (RL), which extends conventional value function approximator (VFA) to take as input not only the state (and action) but also an explicit policy representation. Such an extension enables PeVFA to preserve values of multiple policies at the same time and brings an appealing characteristic, i.e., \emph{value generalization among policies}. We formally analyze the value generalization under Generalized Policy Iteration (GPI). From theoretical and empirical lens, we show that generalized value estimates offered by PeVFA may have lower initial approximation error to true values of successive policies, which is expected to improve consecutive value approximation during GPI. Based on above clues, we introduce a new form of GPI with PeVFA which leverages the value generalization along policy improvement path. Moreover, we propose a representation learning framework for RL policy, providing several approaches to learn effective policy embeddings from policy network parameters or state-action pairs. In our experiments, we evaluate the efficacy of value generalization offered by PeVFA and policy representation learning in several OpenAI Gym continuous control tasks. For a representative instance of algorithm implementation, Proximal Policy Optimization (PPO) re-implemented under the paradigm of GPI with PeVFA achieves about 40\% performance improvement on its vanilla counterpart in most environments.

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Off-policy sampling and experience replay are key for improving sample efficiency and scaling model-free temporal difference learning methods. When combined with function approximation, such as neural networks, this combination is known as the deadly triad and is potentially unstable. Recently, it has been shown that stability and good performance at scale can be achieved by combining emphatic weightings and multi-step updates. This approach, however, is generally limited to sampling complete trajectories in order, to compute the required emphatic weighting. In this paper we investigate how to combine emphatic weightings with non-sequential, off-line data sampled from a replay buffer. We develop a multi-step emphatic weighting that can be combined with replay, and a time-reversed n-step TD learning algorithm to learn the required emphatic weighting. We show that these state weightings reduce variance compared with prior approaches, while providing convergence guarantees. We tested the approach at scale on Atari 2600 video games, and observed that the newX-ETD(n) agent improved over baseline agents, highlighting both the scalability and broad applicability of our approach.

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