Value function approximation has demonstrated phenomenal empirical success in reinforcement learning (RL). Nevertheless, despite a handful of recent progress on developing theory for RL with linear function approximation, the understanding of \emph{general} function approximation schemes largely remains missing. In this paper, we establish the first provably efficient RL algorithm with general value function approximation. We show that if the value functions admit an approximation with a function class $\mathcal{F}$, our algorithm achieves a regret bound of $\widetilde{O}(\mathrm{poly}(dH)\sqrt{T})$ where $d$ is a complexity measure of $\mathcal{F}$ that depends on the eluder dimension~[Russo and Van Roy, 2013] and log-covering numbers, $H$ is the planning horizon, and $T$ is the number interactions with the environment.

It is believed that a model-based approach for reinforcement learning (RL) is the key to reduce sample complexity. However, the understanding of the sample optimality of model-based RL is still largely missing, even for the linear case. This work considers sample complexity of finding an $\epsilon$-optimal policy in a Markov decision process (MDP) that admits a linear additive feature representation, given only access to a generative model. We solve this problem via a plug-in solver approach, which builds an empirical model and plans in this empirical model via an arbitrary plug-in solver. We prove that under the anchor-state assumption, which implies implicit non-negativity in the feature space, the minimax sample complexity of finding an $\epsilon$-optimal policy in a $\gamma$-discounted MDP is $O(K/(1-\gamma)^3\epsilon^2)$, which only depends on the dimensionality $K$ of the feature space and has no dependence on the state or action space. We further extend our results to a relaxed setting where anchor-states may not exist and show that a plug-in approach can be sample efficient as well, providing a flexible approach to design model-based algorithms for RL.

The use of pessimism, when reasoning about datasets lacking exhaustive exploration has recently gained prominence in offline reinforcement learning. Despite the robustness it adds to the algorithm, overly pessimistic reasoning can be equally damaging in precluding the discovery of good policies, which is an issue for the popular bonus-based pessimism. In this paper, we introduce the notion of Bellman-consistent pessimism for general function approximation: instead of calculating a point-wise lower bound for the value function, we implement pessimism at the initial state over the set of functions consistent with the Bellman equations. Our theoretical guarantees only require Bellman closedness as standard in the exploratory setting, in which case bonus-based pessimism fails to provide guarantees. Even in the special case of linear function approximation where stronger expressivity assumptions hold, our result improves upon a recent bonus-based approach by $\mathcal O(d)$ in its sample complexity (when the action space is finite). Remarkably, our algorithms automatically adapt to the best bias-variance tradeoff in the hindsight, whereas most prior approaches require tuning extra hyperparameters a priori.

Generating fluent and relevant language to describe visual content is critical for the video captioning task. Many existing methods generate captions using sequence models that predict words in a left-to-right order. In this paper, we investigate a graph-structured model for caption generation by explicitly modeling the hierarchical structure in the sentences to further improve the fluency and relevance of sentences. To this end, we propose a novel video captioning method that generates a sentence by first constructing a multi-modal dependency tree and then traversing the constructed tree, where the syntactic structure and semantic relationship in the sentence are represented by the tree topology. To take full advantage of the information from both vision and language, both the visual and textual representation features are encoded into each tree node. Different from existing dependency parsing methods that generate uni-modal dependency trees for language understanding, our method construct s multi-modal dependency trees for language generation of images and videos. We also propose a tree-structured reinforcement learning algorithm to effectively optimize the captioning model where a novel reward is designed by evaluating the semantic consistency between the generated sub-tree and the ground-truth tree. Extensive experiments on several video captioning datasets demonstrate the effectiveness of the proposed method.

While deep learning and deep reinforcement learning (RL) systems have demonstrated impressive results in domains such as image classification, game playing, and robotic control, data efficiency remains a major challenge. Multi-task learning has emerged as a promising approach for sharing structure across multiple tasks to enable more efficient learning. However, the multi-task setting presents a number of optimization challenges, making it difficult to realize large efficiency gains compared to learning tasks independently. The reasons why multi-task learning is so challenging compared to single-task learning are not fully understood. In this work, we identify a set of three conditions of the multi-task optimization landscape that cause detrimental gradient interference, and develop a simple yet general approach for avoiding such interference between task gradients. We propose a form of gradient surgery that projects a task's gradient onto the normal plane of the gradient of any other task that has a gradient. On a series of challenging multi-task supervised and multi-task RL problems, this approach leads to substantial gains in efficiency and performance. Further, it is model-agnostic and can be combined with previously-proposed multi-task architectures for enhanced performance.

Reinforcement learning (RL) has shown great promise for developing agents for dialogue management (DM) that are non-myopic, conduct rich conversations, and maximize overall user satisfaction. Despite the advancements in RL and language models (LMs), employing RL to drive conversational chatbots still poses significant challenges. A primary issue stems from RL's dependency on online exploration for effective learning, a process that can be costly. Moreover, engaging in online interactions with humans during the training phase can raise safety concerns, as the LM can potentially generate unwanted outputs. This issue is exacerbated by the combinatorial action spaces facing these algorithms, as most LM agents generate responses at the word level. We develop various RL algorithms, specialized in dialogue planning, that leverage recent Mixture-of-Expert Language Models (MoE-LMs)---models that capture diverse semantics, generate utterances reflecting different intents, and are amenable for multi-turn DM. By exploiting the MoE-LM structure, our methods significantly reduce the size of the action space and improve the efficacy of RL-based DM. We evaluate our methods in open-domain dialogue to demonstrate their effectiveness with respect to the diversity of intent in generated utterances and overall DM performance.

Regardless of the particular task we want to perform in an environment, there are often shared safety constraints we want our agents to respect. For example, regardless of whether it is making a sandwich or clearing the table, a kitchen robot should not break a plate. Manually specifying such a constraint can be both time-consuming and error-prone. We show how to learn constraints from expert demonstrations of safe task completion by extending inverse reinforcement learning (IRL) techniques to the space of constraints. Intuitively, we learn constraints that forbid highly rewarding behavior that the expert could have taken but chose not to. Unfortunately, the constraint learning problem is rather ill-posed and typically leads to overly conservative constraints that forbid all behavior that the expert did not take. We counter this by leveraging diverse demonstrations that naturally occur in multi-task setting to learn a tighter set of constraints.

Learning models of the environment from data is often viewed as an essential component to building intelligent reinforcement learning (RL) agents. The common practice is to separate the learning of the model from its use, by constructing a model of the environment's dynamics that correctly predicts the observed state transitions. In this paper we argue that the limited representational resources of model-based RL agents are better used to build models that are directly useful for value-based planning. As our main contribution, we introduce the principle of value equivalence: two models are value equivalent with respect to a set of functions and policies if they yield the same Bellman updates. We propose a formulation of the model learning problem based on the value equivalence principle and analyze how the set of feasible solutions is impacted by the choice of policies and functions. Specifically, we show that, as we augment the set of policies and functions considered, the class of value equivalent models shrinks, until eventually collapsing to a single point corresponding to a model that perfectly describes the environment.

We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i.e., zero-sum stochastic games). We consider an episodic setting where in each episode, each player independently selects a policy and observes only their own actions and rewards, along with the state. We show that if both players run policy gradient methods in tandem, their policies will converge to a min-max equilibrium of the game, as long as their learning rates follow a two-timescale rule (which is necessary). To the best of our knowledge, this constitutes the first finite-sample convergence result for independent learning in competitive RL, as prior work has largely focused on centralized/coordinated procedures for equilibrium computation.

Due to the inability to interact with the environment, offline reinforcement learning (RL) methods face the challenge of estimating the Out-of-Distribution (OOD) points. Existing methods for addressing this issue either control policy to exclude the OOD action or make the $Q$ function pessimistic. However, these methods can be overly conservative or fail to identify OOD areas accurately. To overcome this problem, we propose a Constrained Policy optimization with Explicit Behavior density (CPED) method that utilizes a flow-GAN model to explicitly estimate the density of behavior policy. By estimating the explicit density, CPED can accurately identify the safe region and enable exploration within the region, resulting in less conservative learning policies. We further provide theoretical results for both the flow-GAN estimator and performance guarantee for CPED by showing that CPED can find the optimal $Q$-function value. Empirically, CPED outperforms existing alternatives on various standard offline reinforcement learning tasks, yielding higher expected returns.