The Bayes-Adaptive Markov Decision Process (BAMDP) formalism pursues the Bayes-optimal solution to the exploration-exploitation trade-off in reinforcement learning. As the computation of exact solutions to Bayesian reinforcement-learning problems is intractable, much of the literature has focused on developing suitable approximation algorithms. In this work, before diving into algorithm design, we first define, under mild structural assumptions, a complexity measure for BAMDP planning. As efficient exploration in BAMDPs hinges upon the judicious acquisition of information, our complexity measure highlights the worst-case difficulty of gathering information and exhausting epistemic uncertainty. To illustrate its significance, we establish a computationally-intractable, exact planning algorithm that takes advantage of this measure to show more efficient planning. We then conclude by introducing a specific form of state abstraction with the potential to reduce BAMDP complexity and gives rise to a computationally-tractable, approximate planning algorithm.

Standard sequential decision-making paradigms aim to maximize the cumulative reward when interacting with the unknown environment., i.e., maximize $\sum_{h = 1}^H r_h$ where $H$ is the planning horizon. However, this paradigm fails to model important practical applications, e.g., safe control that aims to maximize the lowest reward, i.e., maximize $\min_{h= 1}^H r_h$. In this paper, based on techniques in sketching algorithms, we propose a novel planning algorithm in deterministic systems which deals with a large class of objective functions of the form $f(r_1, r_2, ... r_H)$ that are of interest to practical applications. We show that efficient planning is possible if $f$ is symmetric under permutation of coordinates and satisfies certain technical conditions. Complementing our algorithm, we further prove that removing any of the conditions will make the problem intractable in the worst case and thus demonstrate the necessity of our conditions.

Imitation learning is a class of promising policy learning algorithms that is free from many practical issues with reinforcement learning, such as the reward design issue and the exploration hardness. However, the current imitation algorithm struggles to achieve both high performance and high in-environment sample efficiency simultaneously. Behavioral Cloning (BC) does not need in-environment interactions, but it suffers from the covariate shift problem which harms its performance. Adversarial Imitation Learning (AIL) turns imitation learning into a distribution matching problem. It can achieve better performance on some tasks but it requires a large number of in-environment interactions.

Sample-based planning is a powerful family of algorithms for generating intelligent behavior from a model of the environment. Generating good candidate actions is critical to the success of sample-based planners, particularly in continuous or large action spaces. Typically, candidate action generation exhausts the action space, uses domain knowledge, or more recently, involves learning a stochastic policy to provide such search guidance. In this paper we explore explicitly learning a candidate action generator by optimizing a novel objective, marginal utility. The marginal utility of an action generator measures the increase in value of an action over previously generated actions.

We propose MDP-GapE, a new trajectory-based Monte-Carlo Tree Search algorithm for planning in a Markov Decision Process in which transitions have a finite support. We prove an upper bound on the number of sampled trajectories needed for MDP-GapE to identify a near-optimal action with high probability. This problem-dependent result is expressed in terms of the sub-optimality gaps of the state-action pairs that are visited during exploration. Our experiments reveal that MDP-GapE is also effective in practice, in contrast with other algorithms with sample complexity guarantees in the fixed-confidence setting, that are mostly theoretical.

This paper studies a model learning and online planning approach towards building flexible and general robots. Specifically, we investigate how to exploit the locality and sparsity structures in the underlying environmental transition model to improve model generalization, data-efficiency, and runtime-efficiency. We present a new domain definition language, named PDSketch. It allows users to flexibly define high-level structures in the transition models, such as object and feature dependencies, in a way similar to how programmers use TensorFlow or PyTorch to specify kernel sizes and hidden dimensions of a convolutional neural network. The details of the transition model will be filled in by trainable neural networks.

Continual reinforcement learning (CRL) refers to a naturalistic setting where an agent needs to endlessly evolve, by trial and error, to solve multiple tasks that are presented sequentially. One of the largest obstacles to CRL is that the agent may forget how to solve previous tasks when learning a new task, known as catastrophic forgetting. In this paper, we propose to address this challenge by planning with online world models. Specifically, we learn a Follow-The-Leader shallow model online to capture the world dynamics, in which we plan using model predictive control to solve a set of tasks specified by any reward functions. The online world model is immune to forgetting by construction with a proven regret bound of $\mathcal{O}(\sqrt{K^2D\log(T)})$ under mild assumptions. The planner searches actions solely based on the latest online model, thus forming a FTL Online Agent (OA) that updates incrementally. To assess OA, we further design Continual Bench, a dedicated environment for CRL, and compare with several strong baselines under the same model-planning algorithmic framework. The empirical results show that OA learns continuously to solve new tasks while not forgetting old skills, outperforming agents built on deep world models with various continual learning techniques.

Among the most important properties of algorithms investigated in computer science are soundness, completeness, and complexity. These properties, however, are rarely analyzed for the vast collection of recently proposed methods for planning with large language models. In this work, we alleviate this gap. We analyse these properties of using LLMs for planning and highlight that recent trends abandon both soundness and completeness for the sake of inefficiency. We propose a significantly more efficient approach that can, at the same time, maintain both soundness and completeness.

Many potential applications of reinforcement learning (RL) are stymied by the large numbers of samples required to learn an effective policy. This is especially true when applying RL to real-world control tasks, e.g. in the sciences or robotics, where executing a policy in the environment is costly. In popular RL algorithms, agents typically explore either by adding stochasticity to a reward-maximizing policy or by attempting to gather maximal information about environment dynamics without taking the given task into account. In this work, we develop a method that allows us to plan for exploration while taking both the task and the current knowledge about the dynamics into account. The key insight to our approach is to plan an action sequence that maximizes the expected information gain about the optimal trajectory for the task at hand.

Large language models (LLMs) have shown remarkable advancements in enabling language agents to tackle simple tasks. However, applying them for complex, multi-step, long-horizon tasks remains a challenge. Recent work have found success by separating high-level planning from low-level execution, which enables the model to effectively balance high-level planning objectives and low-level execution details. However, generating accurate plans remains difficult since LLMs are not inherently trained for this task. To address this, we propose Plan-and-Act, a novel framework that incorporates explicit planning into LLM-based agents and introduces a scalable method to enhance plan generation through a novel synthetic data generation method. Plan-and-Act consists of a Planner model which generates structured, high-level plans to achieve user goals, and an Executor model that translates these plans into environment-specific actions. To train the Planner effectively, we introduce a synthetic data generation method that annotates ground-truth trajectories with feasible plans, augmented with diverse and extensive examples to enhance generalization. We evaluate Plan-and-Act using web navigation as a representative long-horizon planning environment, demonstrating a state-of the-art 54% success rate on the WebArena-Lite benchmark.