Reinforcement learning algorithms typically consider discrete-time dynamics, even though the underlying systems are often continuous in time. In this paper, we introduce a model-based reinforcement learning algorithm that represents continuous-time dynamics using nonlinear ordinary differential equations (ODEs). We capture epistemic uncertainty using well-calibrated probabilistic models, and use the optimistic principle for exploration. Our regret bounds surface the importance of the measurement selection strategy (MSS), since in continuous time we not only must decide how to explore, but also when to observe the underlying system. Our analysis demonstrates that the regret is sublinear when modeling ODEs with Gaussian Processes (GP) for common choices of MSS, such as equidistant sampling. Additionally, we propose an adaptive, data-dependent, practical MSS that, when combined with GP dynamics, also achieves sublinear regret with significantly fewer samples. We showcase the benefits of continuous-time modeling over its discrete-time counterpart, as well as our proposed adaptive MSS over standard baselines, on several applications.

Efficient exploration is crucial to achieving good performance in reinforcement learning. Existing systematic exploration strategies (R-MAX, MBIE, UCRL, etc.), despite being promising theoretically, are essentially greedy strategies that follow some predefined heuristics. When the heuristics do not match the dynamics of Markov decision processes (MDPs) well, an excessive amount of time can be wasted in travelling through already-explored states, lowering the overall efficiency. We argue that explicit planning for exploration can help alleviate such a problem, and propose a Value Iteration for Exploration Cost (VIEC) algorithm which computes the optimal exploration scheme by solving an augmented MDP. We then present a detailed analysis of the exploration behaviour of some popular strategies, showing how these strategies can fail and spend O(n^2 md) or O(n^2 m + nmd) steps to collect sufficient data in some tower-shaped MDPs, while the optimal exploration scheme, which can be obtained by VIEC, only needs O(nmd), where n, m are the numbers of states and actions and d is the data demand. The analysis not only points out the weakness of existing heuristic-based strategies, but also suggests a remarkable potential in explicit planning for exploration.

In reinforcement learning, pre-trained low-level skills have the potential to greatly facilitate exploration. However, prior knowledge of the downstream task is required to strike the right balance between generality (fine-grained control) and specificity (faster learning) in skill design. In previous work on continuous control, the sensitivity of methods to this trade-off has not been addressed explicitly, as locomotion provides a suitable prior for navigation tasks, which have been of foremost interest. In this work, we analyze this trade-off for low-level policy pre-training with a new benchmark suite of diverse, sparse-reward tasks for bipedal robots. We alleviate the need for prior knowledge by proposing a hierarchical skill learning framework that acquires skills of varying complexity in an unsupervised manner. For utilization on downstream tasks, we present a three-layered hierarchical learning algorithm to automatically trade off between general and specific skills as required by the respective task. In our experiments, we show that our approach performs this trade-off effectively and achieves better results than current state-of-the-art methods for end-to-end hierarchical reinforcement learning and unsupervised skill discovery.

The problem of inverse reinforcement learning (IRL) is relevant to a variety of tasks including value alignment and robot learning from demonstration. Despite significant algorithmic contributions in recent years, IRL remains an ill-posed problem at its core; multiple reward functions coincide with the observed behavior and the actual reward function is not identifiable without prior knowledge or supplementary information. This paper presents an IRL framework called Bayesian optimization-IRL (BO-IRL) which identifies multiple solutions that are consistent with the expert demonstrations by efficiently exploring the reward function space. BO-IRL achieves this by utilizing Bayesian Optimization along with our newly proposed kernel that (a) projects the parameters of policy invariant reward functions to a single point in a latent space and (b) ensures nearby points in the latent space correspond to reward functions yielding similar likelihoods. This projection allows the use of standard stationary kernels in the latent space to capture the correlations present across the reward function space. Empirical results on synthetic and real-world environments (model-free and model-based) show that BO-IRL discovers multiple reward functions while minimizing the number of expensive exact policy optimizations.

Reinforcement Learning (RL) has shown remarkable success in enhancing the reasoning capabilities of Large Language Models (LLMs). Process-Supervised RL (PSRL) has emerged as a more effective paradigm compared to outcome-based RL. However, existing PSRL approaches suffer from limited exploration efficiency, both in terms of branching positions and sampling. In this paper, we introduce a novel PSRL framework (AttnRL), which enables efficient exploration for reasoning models. Motivated by preliminary observations that steps exhibiting high attention scores correlate with reasoning behaviors, we propose to branch from positions with high values. Furthermore, we develop an adaptive sampling strategy that accounts for problem difficulty and historical batch size, ensuring that the whole training batch maintains non-zero advantage values. To further improve sampling efficiency, we design a one-step off-policy training pipeline for PSRL. Extensive experiments on multiple challenging mathematical reasoning benchmarks demonstrate that our method consistently outperforms prior approaches in terms of performance and sampling and training efficiency.

We consider the problem of reinforcement learning over episodes of a finite-horizon deterministic system and as a solution propose optimistic constraint propagation (OCP), an algorithm designed to synthesize efficient exploration and value function generalization. We establish that when the true value function lies within the given hypothesis class, OCP selects optimal actions over all but at most K episodes, where K is the eluder dimension of the given hypothesis class. We establish further efficiency and asymptotic performance guarantees that apply even if the true value function does not lie in the given hypothesis space, for the special case where the hypothesis space is the span of pre-specified indicator functions over disjoint sets.

We study the problem of nonepisodic reinforcement learning (RL) for nonlinear dynamical systems, where the system dynamics are unknown and the RL agent has to learn from a single trajectory, i.e., without resets. We propose **N**on**e**pisodic **O**ptistmic **RL** (NeoRL), an approach based on the principle of optimism in the face of uncertainty. NeoRL uses well-calibrated probabilistic models and plans optimistically w.r.t. the epistemic uncertainty about the unknown dynamics. Under continuity and bounded energy assumptions on the system, weprovide a first-of-its-kind regret bound of \mathcal{O}(\beta_T \sqrt{T \Gamma_T}) for general nonlinear systems with Gaussian process dynamics. We compare NeoRL to other baselines on several deep RL environments and empirically demonstrate that NeoRL achieves the optimal average cost while incurring the least regret.

I would just like to confirm my understanding of the algorithmic contributions of this work. As far as I understand, Jin et al [2019] propose a learning algorithm for the standard RL case with linear function approximation in linear MDPs. Then Jin et al [2020] propose a method for efficient exploration in the reward-free RL case. This is for normal MDPs but in the tabular setting. In that work, exploration is achieved by constructing a reward function where the reward is 1 for states that are "significant", and 0 otherwise, and then solving the resulting task with an efficient learning algorithm.

This paper introduces the interesting idea of demand matrices to more efficiently do pure exploration. Demand matrices simply specific the minimum number of times needed to visit every state-action pair. This is then treated as an additional part of the state in an augmented MDP, which can then be solved to derive the optimal exploration strategy to achieve the specified initial demand. While the idea is interesting and solid, there are downsides to the idea itself and some of the analysis in this paper that could be improved upon. There are no theoretical guarantees that using this algorithm with a learned model at the same time will work.