We consider the problem of tabular infinite horizon concave utility reinforcement learning (CURL) with convex constraints. Various learning applications with constraints, such as robotics, do not allow for policies that can violate constraints. To this end, we propose a model-based learning algorithm that achieves zero constraint violations. To obtain this result, we assume that the concave objective and the convex constraints have a solution interior to the set of feasible occupation measures. We then solve a tighter optimization problem to ensure that the constraints are never violated despite the imprecise model knowledge and model stochasticity. We also propose a novel Bellman error based analysis for tabular infinite-horizon setups which allows to analyse stochastic policies. Combining the Bellman error based analysis and tighter optimization equation, for $T$ interactions with the environment, we obtain a regret guarantee for objective which grows as $\Tilde{O}(1/\sqrt{T})$, excluding other factors.
相關內容
Despite the increasing popularity of policy gradient methods, they are yet to be widely utilized in sample-scarce applications, such as robotics. The sample efficiency could be improved by making best usage of available information. As a key component in reinforcement learning, the reward function is usually devised carefully to guide the agent. Hence, the reward function is usually known, allowing access to not only scalar reward signals but also reward gradients. To benefit from reward gradients, previous works require the knowledge of environment dynamics, which are hard to obtain. In this work, we develop the \textit{Reward Policy Gradient} estimator, a novel approach that integrates reward gradients without learning a model. Bypassing the model dynamics allows our estimator to achieve a better bias-variance trade-off, which results in a higher sample efficiency, as shown in the empirical analysis. Our method also boosts the performance of Proximal Policy Optimization on different MuJoCo control tasks.
Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current algorithms over-fit to the training dataset and as a consequence perform poorly when deployed to out-of-distribution generalizations of the environment. We aim to address these limitations by learning a Koopman latent representation which allows us to infer symmetries of the system's underlying dynamic. The latter is then utilized to extend the otherwise static offline dataset during training; this constitutes a novel data augmentation framework which reflects the system's dynamic and is thus to be interpreted as an exploration of the environments phase space. To obtain the symmetries we employ Koopman theory in which nonlinear dynamics are represented in terms of a linear operator acting on the space of measurement functions of the system and thus symmetries of the dynamics may be inferred directly. We provide novel theoretical results on the existence and nature of symmetries relevant for control systems such as reinforcement learning settings. Moreover, we empirically evaluate our method on several benchmark offline reinforcement learning tasks and datasets including D4RL, Metaworld and Robosuite and find that by using our framework we consistently improve the state-of-the-art for Q-learning methods.
Policy optimization, which learns the policy of interest by maximizing the value function via large-scale optimization techniques, lies at the heart of modern reinforcement learning (RL). In addition to value maximization, other practical considerations arise commonly as well, including the need of encouraging exploration, and that of ensuring certain structural properties of the learned policy due to safety, resource and operational constraints. These considerations can often be accounted for by resorting to regularized RL, which augments the target value function with a structure-promoting regularization term. Focusing on an infinite-horizon discounted Markov decision process, this paper proposes a generalized policy mirror descent (GPMD) algorithm for solving regularized RL. As a generalization of policy mirror descent Lan (2021), the proposed algorithm accommodates a general class of convex regularizers as well as a broad family of Bregman divergence in cognizant of the regularizer in use. We demonstrate that our algorithm converges linearly over an entire range of learning rates, in a dimension-free fashion, to the global solution, even when the regularizer lacks strong convexity and smoothness. In addition, this linear convergence feature is provably stable in the face of inexact policy evaluation and imperfect policy updates. Numerical experiments are provided to corroborate the applicability and appealing performance of GPMD.
Multi-agent reinforcement learning (MARL) problems are challenging due to information asymmetry. To overcome this challenge, existing methods often require high level of coordination or communication between the agents. We consider two-agent multi-armed bandits (MABs) and Markov decision processes (MDPs) with a hierarchical information structure arising in applications, which we exploit to propose simpler and more efficient algorithms that require no coordination or communication. In the structure, in each step the ``leader" chooses her action first, and then the ``follower" decides his action after observing the leader's action. The two agents observe the same reward (and the same state transition in the MDP setting) that depends on their joint action. For the bandit setting, we propose a hierarchical bandit algorithm that achieves a near-optimal gap-independent regret of $\widetilde{\mathcal{O}}(\sqrt{ABT})$ and a near-optimal gap-dependent regret of $\mathcal{O}(\log(T))$, where $A$ and $B$ are the numbers of actions of the leader and the follower, respectively, and $T$ is the number of steps. We further extend to the case of multiple followers and the case with a deep hierarchy, where we both obtain near-optimal regret bounds. For the MDP setting, we obtain $\widetilde{\mathcal{O}}(\sqrt{H^7S^2ABT})$ regret, where $H$ is the number of steps per episode, $S$ is the number of states, $T$ is the number of episodes. This matches the existing lower bound in terms of $A, B$, and $T$.
Traditional machine learning relies on a centralized data pipeline, i.e., data are provided to a central server for model training. In many applications, however, data are inherently fragmented. Such a decentralized nature of these databases presents the biggest challenge for collaboration: sending all decentralized datasets to a central server raises serious privacy concerns. Although there has been a joint effort in tackling such a critical issue by proposing privacy-preserving machine learning frameworks, such as federated learning, most state-of-the-art frameworks are built still in a centralized way, in which a central client is needed for collecting and distributing model information (instead of data itself) from every other client, leading to high communication pressure and high vulnerability when there exists a failure at or attack on the central client. Here we propose a principled decentralized federated learning algorithm (DeceFL), which does not require a central client and relies only on local information transmission between clients and their neighbors, representing a fully decentralized learning framework. It has been further proven that every client reaches the global minimum with zero performance gap and achieves the same convergence rate $O(1/T)$ (where $T$ is the number of iterations in gradient descent) as centralized federated learning when the loss function is smooth and strongly convex. Finally, the proposed algorithm has been applied to a number of applications to illustrate its effectiveness for both convex and nonconvex loss functions, demonstrating its applicability to a wide range of real-world medical and industrial applications.
We study constrained reinforcement learning (CRL) from a novel perspective by setting constraints directly on state density functions, rather than the value functions considered by previous works. State density has a clear physical and mathematical interpretation, and is able to express a wide variety of constraints such as resource limits and safety requirements. Density constraints can also avoid the time-consuming process of designing and tuning cost functions required by value function-based constraints to encode system specifications. We leverage the duality between density functions and Q functions to develop an effective algorithm to solve the density constrained RL problem optimally and the constrains are guaranteed to be satisfied. We prove that the proposed algorithm converges to a near-optimal solution with a bounded error even when the policy update is imperfect. We use a set of comprehensive experiments to demonstrate the advantages of our approach over state-of-the-art CRL methods, with a wide range of density constrained tasks as well as standard CRL benchmarks such as Safety-Gym.
In real world settings, numerous constraints are present which are hard to specify mathematically. However, for the real world deployment of reinforcement learning (RL), it is critical that RL agents are aware of these constraints, so that they can act safely. In this work, we consider the problem of learning constraints from demonstrations of a constraint-abiding agent's behavior. We experimentally validate our approach and show that our framework can successfully learn the most likely constraints that the agent respects. We further show that these learned constraints are \textit{transferable} to new agents that may have different morphologies and/or reward functions. Previous works in this regard have either mainly been restricted to tabular (discrete) settings, specific types of constraints or assume the environment's transition dynamics. In contrast, our framework is able to learn arbitrary \textit{Markovian} constraints in high-dimensions in a completely model-free setting. The code can be found it: \url{//github.com/shehryar-malik/icrl}.
Recent successes of value-based multi-agent deep reinforcement learning employ optimism in value function by carefully controlling learning rate(Omidshafiei et al., 2017) or reducing update prob-ability (Palmer et al., 2018). We introduce a de-centralized quantile estimator: Responsible Implicit Quantile Network (RIQN), while robust to teammate-environment interactions, able to reduce the amount of imposed optimism. Upon benchmarking against related Hysteretic-DQN(HDQN) and Lenient-DQN (LDQN), we findRIQN agents more stable, sample efficient and more likely to converge to the optimal policy.
This paper proposes a model-free Reinforcement Learning (RL) algorithm to synthesise policies for an unknown Markov Decision Process (MDP), such that a linear time property is satisfied. We convert the given property into a Limit Deterministic Buchi Automaton (LDBA), then construct a synchronized MDP between the automaton and the original MDP. According to the resulting LDBA, a reward function is then defined over the state-action pairs of the product MDP. With this reward function, our algorithm synthesises a policy whose traces satisfies the linear time property: as such, the policy synthesis procedure is "constrained" by the given specification. Additionally, we show that the RL procedure sets up an online value iteration method to calculate the maximum probability of satisfying the given property, at any given state of the MDP - a convergence proof for the procedure is provided. Finally, the performance of the algorithm is evaluated via a set of numerical examples. We observe an improvement of one order of magnitude in the number of iterations required for the synthesis compared to existing approaches.
We consider the multi-agent reinforcement learning setting with imperfect information in which each agent is trying to maximize its own utility. The reward function depends on the hidden state (or goal) of both agents, so the agents must infer the other players' hidden goals from their observed behavior in order to solve the tasks. We propose a new approach for learning in these domains: Self Other-Modeling (SOM), in which an agent uses its own policy to predict the other agent's actions and update its belief of their hidden state in an online manner. We evaluate this approach on three different tasks and show that the agents are able to learn better policies using their estimate of the other players' hidden states, in both cooperative and adversarial settings.
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