Many existing reinforcement learning (RL) methods employ stochastic gradient iteration on the back end, whose stability hinges upon a hypothesis that the data-generating process mixes exponentially fast with a rate parameter that appears in the step-size selection. Unfortunately, this assumption is violated for large state spaces or settings with sparse rewards, and the mixing time is unknown, making the step size inoperable. In this work, we propose an RL methodology attuned to the mixing time by employing a multi-level Monte Carlo estimator for the critic, the actor, and the average reward embedded within an actor-critic (AC) algorithm. This method, which we call \textbf{M}ulti-level \textbf{A}ctor-\textbf{C}ritic (MAC), is developed especially for infinite-horizon average-reward settings and neither relies on oracle knowledge of the mixing time in its parameter selection nor assumes its exponential decay; it, therefore, is readily applicable to applications with slower mixing times. Nonetheless, it achieves a convergence rate comparable to the state-of-the-art AC algorithms. We experimentally show that these alleviated restrictions on the technical conditions required for stability translate to superior performance in practice for RL problems with sparse rewards.
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Most video restoration networks are slow, have high computational load, and can't be used for real-time video enhancement. In this work, we design an efficient and fast framework to perform real-time video enhancement for practical use-cases like live video calls and video streams. Our proposed method, called Recurrent Bottleneck Mixer Network (ReBotNet), employs a dual-branch framework. The first branch learns spatio-temporal features by tokenizing the input frames along the spatial and temporal dimensions using a ConvNext-based encoder and processing these abstract tokens using a bottleneck mixer. To further improve temporal consistency, the second branch employs a mixer directly on tokens extracted from individual frames. A common decoder then merges the features form the two branches to predict the enhanced frame. In addition, we propose a recurrent training approach where the last frame's prediction is leveraged to efficiently enhance the current frame while improving temporal consistency. To evaluate our method, we curate two new datasets that emulate real-world video call and streaming scenarios, and show extensive results on multiple datasets where ReBotNet outperforms existing approaches with lower computations, reduced memory requirements, and faster inference time.
Multi-objective reinforcement learning (MORL) algorithms tackle sequential decision problems where agents may have different preferences over (possibly conflicting) reward functions. Such algorithms often learn a set of policies (each optimized for a particular agent preference) that can later be used to solve problems with novel preferences. We introduce a novel algorithm that uses Generalized Policy Improvement (GPI) to define principled, formally-derived prioritization schemes that improve sample-efficient learning. They implement active-learning strategies by which the agent can (i) identify the most promising preferences/objectives to train on at each moment, to more rapidly solve a given MORL problem; and (ii) identify which previous experiences are most relevant when learning a policy for a particular agent preference, via a novel Dyna-style MORL method. We prove our algorithm is guaranteed to always converge to an optimal solution in a finite number of steps, or an $\epsilon$-optimal solution (for a bounded $\epsilon$) if the agent is limited and can only identify possibly sub-optimal policies. We also prove that our method monotonically improves the quality of its partial solutions while learning. Finally, we introduce a bound that characterizes the maximum utility loss (with respect to the optimal solution) incurred by the partial solutions computed by our method throughout learning. We empirically show that our method outperforms state-of-the-art MORL algorithms in challenging multi-objective tasks, both with discrete and continuous state and action spaces.
The chase procedure is a fundamental algorithmic tool in databases that allows us to reason with constraints, such as existential rules, with a plethora of applications. It takes as input a database and a set of constraints, and iteratively completes the database as dictated by the constraints. A key challenge, though, is the fact that it may not terminate, which leads to the problem of checking whether it terminates given a database and a set of constraints. In this work, we focus on the semi-oblivious version of the chase, which is well-suited for practical implementations, and linear existential rules, a central class of constraints with several applications. In this setting, there is a mature body of theoretical work that provides syntactic characterizations of when the chase terminates, algorithms for checking chase termination, precise complexity results, and worst-case optimal bounds on the size of the result of the chase (whenever is finite). Our main objective is to experimentally evaluate the existing chase termination algorithms with the aim of understanding which input parameters affect their performance, clarifying whether they can be used in practice, and revealing their performance limitations.
Offline RL methods have been shown to reduce the need for environment interaction by training agents using offline collected episodes. However, these methods typically require action information to be logged during data collection, which can be difficult or even impossible in some practical cases. In this paper, we investigate the potential of using action-free offline datasets to improve online reinforcement learning, name this problem Reinforcement Learning with Action-Free Offline Pretraining (AFP-RL). We introduce Action-Free Guide (AF-Guide), a method that guides online training by extracting knowledge from action-free offline datasets. AF-Guide consists of an Action-Free Decision Transformer (AFDT) implementing a variant of Upside-Down Reinforcement Learning. It learns to plan the next states from the offline dataset, and a Guided Soft Actor-Critic (Guided SAC) that learns online with guidance from AFDT. Experimental results show that AF-Guide can improve sample efficiency and performance in online training thanks to the knowledge from the action-free offline dataset. Code is available at //github.com/Vision-CAIR/AF-Guide.
Learning Stationary Nash Equilibrium Policies in $n$-Player Stochastic Games with Independent Chains
We consider a subclass of $n$-player stochastic games, in which players have their own internal state/action spaces while they are coupled through their payoff functions. It is assumed that players' internal chains are driven by independent transition probabilities. Moreover, players can receive only realizations of their payoffs, not the actual functions, and cannot observe each other's states/actions. For this class of games, we first show that finding a stationary Nash equilibrium (NE) policy without any assumption on the reward functions is interactable. However, for general reward functions, we develop polynomial-time learning algorithms based on dual averaging and dual mirror descent, which converge in terms of the averaged Nikaido-Isoda distance to the set of $\epsilon$-NE policies almost surely or in expectation. In particular, under extra assumptions on the reward functions such as social concavity, we derive polynomial upper bounds on the number of iterates to achieve an $\epsilon$-NE policy with high probability. Finally, we evaluate the effectiveness of the proposed algorithms in learning $\epsilon$-NE policies using numerical experiments for energy management in smart grids.
Instance segmentation is an important computer vision problem which remains challenging despite impressive recent advances due to deep learning-based methods. Given sufficient training data, fully supervised methods can yield excellent performance, but annotation of ground-truth data remains a major bottleneck, especially for biomedical applications where it has to be performed by domain experts. The amount of labels required can be drastically reduced by using rules derived from prior knowledge to guide the segmentation. However, these rules are in general not differentiable and thus cannot be used with existing methods. Here, we relax this requirement by using stateless actor critic reinforcement learning, which enables non-differentiable rewards. We formulate the instance segmentation problem as graph partitioning and the actor critic predicts the edge weights driven by the rewards, which are based on the conformity of segmented instances to high-level priors on object shape, position or size. The experiments on toy and real datasets demonstrate that we can achieve excellent performance without any direct supervision based only on a rich set of priors.
We study the corrupted bandit problem, i.e. a stochastic multi-armed bandit problem with $k$ unknown reward distributions, which are heavy-tailed and corrupted by a history-independent adversary or Nature. To be specific, the reward obtained by playing an arm comes from corresponding heavy-tailed reward distribution with probability $1-\varepsilon \in (0.5,1]$ and an arbitrary corruption distribution of unbounded support with probability $\varepsilon \in [0,0.5)$. First, we provide $\textit{a problem-dependent lower bound on the regret}$ of any corrupted bandit algorithm. The lower bounds indicate that the corrupted bandit problem is harder than the classical stochastic bandit problem with sub-Gaussian or heavy-tail rewards. Following that, we propose a novel UCB-type algorithm for corrupted bandits, namely HubUCB, that builds on Huber's estimator for robust mean estimation. Leveraging a novel concentration inequality of Huber's estimator, we prove that HubUCB achieves a near-optimal regret upper bound. Since computing Huber's estimator has quadratic complexity, we further introduce a sequential version of Huber's estimator that exhibits linear complexity. We leverage this sequential estimator to design SeqHubUCB that enjoys similar regret guarantees while reducing the computational burden. Finally, we experimentally illustrate the efficiency of HubUCB and SeqHubUCB in solving corrupted bandits for different reward distributions and different levels of corruptions.
Hierarchical learning algorithms that gradually approximate a solution to a data-driven optimization problem are essential to decision-making systems, especially under limitations on time and computational resources. In this study, we introduce a general-purpose hierarchical learning architecture that is based on the progressive partitioning of a possibly multi-resolution data space. The optimal partition is gradually approximated by solving a sequence of optimization sub-problems that yield a sequence of partitions with increasing number of subsets. We show that the solution of each optimization problem can be estimated online using gradient-free stochastic approximation updates. As a consequence, a function approximation problem can be defined within each subset of the partition and solved using the theory of two-timescale stochastic approximation algorithms. This simulates an annealing process and defines a robust and interpretable heuristic method to gradually increase the complexity of the learning architecture in a task-agnostic manner, giving emphasis to regions of the data space that are considered more important according to a predefined criterion. Finally, by imposing a tree structure in the progression of the partitions, we provide a means to incorporate potential multi-resolution structure of the data space into this approach, significantly reducing its complexity, while introducing hierarchical variable-rate feature extraction properties similar to certain classes of deep learning architectures. Asymptotic convergence analysis and experimental results are provided for supervised and unsupervised learning problems.
Consider this scenario: an agent navigates a latent graph by performing actions that take it from one node to another. The chosen action determines the probability distribution over the next visited node. At each node, the agent receives an observation, but this observation is not unique, so it does not identify the node, making the problem aliased. The purpose of this work is to provide a policy that approximately maximizes exploration efficiency (i.e., how well the graph is recovered for a given exploration budget). In the unaliased case, we show improved performance w.r.t. state-of-the-art reinforcement learning baselines. For the aliased case we are not aware of suitable baselines and instead show faster recovery w.r.t. a random policy for a wide variety of topologies, and exponentially faster recovery than a random policy for challenging topologies. We dub the algorithm eFeX (from eFficient eXploration).
In this paper, we address the following problem: Given an offline demonstration dataset from an imperfect expert, what is the best way to leverage it to bootstrap online learning performance in MDPs. We first propose an Informed Posterior Sampling-based RL (iPSRL) algorithm that uses the offline dataset, and information about the expert's behavioral policy used to generate the offline dataset. Its cumulative Bayesian regret goes down to zero exponentially fast in N, the offline dataset size if the expert is competent enough. Since this algorithm is computationally impractical, we then propose the iRLSVI algorithm that can be seen as a combination of the RLSVI algorithm for online RL, and imitation learning. Our empirical results show that the proposed iRLSVI algorithm is able to achieve significant reduction in regret as compared to two baselines: no offline data, and offline dataset but used without information about the generative policy. Our algorithm bridges online RL and imitation learning for the first time.
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