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We propose the homotopic policy mirror descent (HPMD) method for solving discounted, infinite horizon MDPs with finite state and action space, and study its policy convergence. We report three properties that seem to be new in the literature of policy gradient methods: (1) The policy first converges linearly, then superlinearly with order $\gamma^{-2}$ to the set of optimal policies, after $\mathcal{O}(\log(1/\Delta^*))$ number of iterations, where $\Delta^*$ is defined via a gap quantity associated with the optimal state-action value function; (2) HPMD also exhibits last-iterate convergence, with the limiting policy corresponding exactly to the optimal policy with the maximal entropy for every state. No regularization is added to the optimization objective and hence the second observation arises solely as an algorithmic property of the homotopic policy gradient method. (3) For the stochastic HPMD method, we further demonstrate a better than $\mathcal{O}(|\mathcal{S}| |\mathcal{A}| / \epsilon^2)$ sample complexity for small optimality gap $\epsilon$, when assuming a generative model for policy evaluation.

Multi-agent reinforcement learning (MARL) can model many real world applications. However, many MARL approaches rely on epsilon greedy for exploration, which may discourage visiting advantageous states in hard scenarios. In this paper, we propose a new approach QMIX(SEG) for tackling MARL. It makes use of the value function factorization method QMIX to train per-agent policies and a novel Semantic Epsilon Greedy (SEG) exploration strategy. SEG is a simple extension to the conventional epsilon greedy exploration strategy, yet it is experimentally shown to greatly improve the performance of MARL. We first cluster actions into groups of actions with similar effects and then use the groups in a bi-level epsilon greedy exploration hierarchy for action selection. We argue that SEG facilitates semantic exploration by exploring in the space of groups of actions, which have richer semantic meanings than atomic actions. Experiments show that QMIX(SEG) largely outperforms QMIX and leads to strong performance competitive with current state-of-the-art MARL approaches on the StarCraft Multi-Agent Challenge (SMAC) benchmark.

We consider a network of agents. Associated with each agent are her covariate and outcome. Agents influence each other's outcomes according to a certain connection/influence structure. A subset of the agents participate on a platform, and hence, are observable to it. The rest are not observable to the platform and are called the latent agents. The platform does not know the influence structure of the observable or the latent parts of the network. It only observes the data on past covariates and decisions of the observable agents. Observable agents influence each other both directly and indirectly through the influence they exert on the latent agents. We investigate how the platform can estimate the dependence of the observable agents' outcomes on their covariates, taking the latent agents into account. First, we show that this relationship can be succinctly captured by a matrix and provide an algorithm for estimating it under a suitable approximate sparsity condition using historical data of covariates and outcomes for the observable agents. We also obtain convergence rates for the proposed estimator despite the high dimensionality that allows more agents than observations. Second, we show that the approximate sparsity condition holds under the standard conditions used in the literature. Hence, our results apply to a large class of networks. Finally, we apply our results to two practical settings: targeted advertising and promotional pricing. We show that by using the available historical data with our estimator, it is possible to obtain asymptotically optimal advertising/pricing decisions, despite the presence of latent agents.

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to guarantee both optimism and convergence of the associated value iteration scheme. We prove that EB-SSP achieves the minimax regret rate $\widetilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the number of episodes, $S$ is the number of states, $A$ is the number of actions and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of $B_{\star}$, nor of $T_{\star}$ which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of $T_{\star}$ is available) where the regret only contains a logarithmic dependence on $T_{\star}$, thus yielding the first horizon-free regret bound beyond the finite-horizon MDP setting.

To rapidly learn a new task, it is often essential for agents to explore efficiently -- especially when performance matters from the first timestep. One way to learn such behaviour is via meta-learning. Many existing methods however rely on dense rewards for meta-training, and can fail catastrophically if the rewards are sparse. Without a suitable reward signal, the need for exploration during meta-training is exacerbated. To address this, we propose HyperX, which uses novel reward bonuses for meta-training to explore in approximate hyper-state space (where hyper-states represent the environment state and the agent's task belief). We show empirically that HyperX meta-learns better task-exploration and adapts more successfully to new tasks than existing methods.

We study the offline meta-reinforcement learning (OMRL) problem, a paradigm which enables reinforcement learning (RL) algorithms to quickly adapt to unseen tasks without any interactions with the environments, making RL truly practical in many real-world applications. This problem is still not fully understood, for which two major challenges need to be addressed. First, offline RL usually suffers from bootstrapping errors of out-of-distribution state-actions which leads to divergence of value functions. Second, meta-RL requires efficient and robust task inference learned jointly with control policy. In this work, we enforce behavior regularization on learned policy as a general approach to offline RL, combined with a deterministic context encoder for efficient task inference. We propose a novel negative-power distance metric on bounded context embedding space, whose gradients propagation is detached from the Bellman backup. We provide analysis and insight showing that some simple design choices can yield substantial improvements over recent approaches involving meta-RL and distance metric learning. To the best of our knowledge, our method is the first model-free and end-to-end OMRL algorithm, which is computationally efficient and demonstrated to outperform prior algorithms on several meta-RL benchmarks.

We consider the exploration-exploitation trade-off in reinforcement learning and we show that an agent imbued with a risk-seeking utility function is able to explore efficiently, as measured by regret. The parameter that controls how risk-seeking the agent is can be optimized exactly, or annealed according to a schedule. We call the resulting algorithm K-learning and show that the corresponding K-values are optimistic for the expected Q-values at each state-action pair. The K-values induce a natural Boltzmann exploration policy for which the `temperature' parameter is equal to the risk-seeking parameter. This policy achieves an expected regret bound of $\tilde O(L^{3/2} \sqrt{S A T})$, where $L$ is the time horizon, $S$ is the number of states, $A$ is the number of actions, and $T$ is the total number of elapsed time-steps. This bound is only a factor of $L$ larger than the established lower bound. K-learning can be interpreted as mirror descent in the policy space, and it is similar to other well-known methods in the literature, including Q-learning, soft-Q-learning, and maximum entropy policy gradient, and is closely related to optimism and count based exploration methods. K-learning is simple to implement, as it only requires adding a bonus to the reward at each state-action and then solving a Bellman equation. We conclude with a numerical example demonstrating that K-learning is competitive with other state-of-the-art algorithms in practice.

This work considers the problem of provably optimal reinforcement learning for episodic finite horizon MDPs, i.e. how an agent learns to maximize his/her long term reward in an uncertain environment. The main contribution is in providing a novel algorithm --- Variance-reduced Upper Confidence Q-learning (vUCQ) --- which enjoys a regret bound of $\widetilde{O}(\sqrt{HSAT} + H^5SA)$, where the $T$ is the number of time steps the agent acts in the MDP, $S$ is the number of states, $A$ is the number of actions, and $H$ is the (episodic) horizon time. This is the first regret bound that is both sub-linear in the model size and asymptotically optimal. The algorithm is sub-linear in that the time to achieve $\epsilon$-average regret for any constant $\epsilon$ is $O(SA)$, which is a number of samples that is far less than that required to learn any non-trivial estimate of the transition model (the transition model is specified by $O(S^2A)$ parameters). The importance of sub-linear algorithms is largely the motivation for algorithms such as $Q$-learning and other "model free" approaches. vUCQ algorithm also enjoys minimax optimal regret in the long run, matching the $\Omega(\sqrt{HSAT})$ lower bound. Variance-reduced Upper Confidence Q-learning (vUCQ) is a successive refinement method in which the algorithm reduces the variance in $Q$-value estimates and couples this estimation scheme with an upper confidence based algorithm. Technically, the coupling of both of these techniques is what leads to the algorithm enjoying both the sub-linear regret property and the asymptotically optimal regret.

Deep reinforcement learning (RL) methods generally engage in exploratory behavior through noise injection in the action space. An alternative is to add noise directly to the agent's parameters, which can lead to more consistent exploration and a richer set of behaviors. Methods such as evolutionary strategies use parameter perturbations, but discard all temporal structure in the process and require significantly more samples. Combining parameter noise with traditional RL methods allows to combine the best of both worlds. We demonstrate that both off- and on-policy methods benefit from this approach through experimental comparison of DQN, DDPG, and TRPO on high-dimensional discrete action environments as well as continuous control tasks. Our results show that RL with parameter noise learns more efficiently than traditional RL with action space noise and evolutionary strategies individually.

This paper presents a safety-aware learning framework that employs an adaptive model learning method together with barrier certificates for systems with possibly nonstationary agent dynamics. To extract the dynamic structure of the model, we use a sparse optimization technique, and the resulting model will be used in combination with control barrier certificates which constrain feedback controllers only when safety is about to be violated. Under some mild assumptions, solutions to the constrained feedback-controller optimization are guaranteed to be globally optimal, and the monotonic improvement of a feedback controller is thus ensured. In addition, we reformulate the (action-)value function approximation to make any kernel-based nonlinear function estimation method applicable. We then employ a state-of-the-art kernel adaptive filtering technique for the (action-)value function approximation. The resulting framework is verified experimentally on a brushbot, whose dynamics is unknown and highly complex.