A.1 Additional lemma Lemma 9 Let s0 be the starting state, let (a)n represent a sequence of actions and let M = Z(ar)Z(ar 1)...Z(a1) i.e., the product of matrices in {Z(a)}left multiplied in order of the sequence Proof Here we use proof by induction. We note that the interchange of the integral and infinite summation is justified by Section 3.7 in [5], since the coefficients Z We can then conclude the statement of the lemma by induction. A.2 Proof of Proposition 1 Proof By Lemma 9, given a fixed sequence of actions (a)n, the r-th state sr under this sequence of actions starting from state s0 has a distribution that can be represented over the basis {φn(s)}. Therefore, the expected reward under any sequence of actions for reward Ris the same as for the projected reward R0 for any state sr where r > 0. The reward at the starting state, R(s0) does not depend on the policy. Therefore, the value of R(s0) does not change whether a policy is optimal or not.

Training automated agents to complete complex tasks in interactive environments is challenging: reinforcement learning requires careful hand-engineering of reward functions, imitation learning requires specialized infrastructure and access to a human expert, and learning from intermediate forms of supervision (like binary preferences) is time-consuming and extracts little information from each human intervention. Can we overcome these challenges by building agents that learn from rich, interactive feedback instead? We propose a new supervision paradigm for interactive learning based on "teachable" decision-making systems that learn from structured advice provided by an external teacher. We begin by formalizing a class of human-in-the-loop decision making problems in which multiple forms of teacher-provided advice are available to a learner. We then describe a simple learning algorithm for these problems that first learns to interpret advice, then learns from advice to complete tasks even in the absence of human supervision. In puzzle-solving, navigation, and locomotion domains, we show that agents that learn from advice can acquire new skills with significantly less human supervision than standard reinforcement learning algorithms and often less than imitation learning.

Simulation is used extensively in autonomous systems, particularly in robotic manipulation. By far, the most common approach is to train a controller in simulation, and then use it as an initial starting point for the real system. We demonstrate how to learn simultaneously from both simulation and interaction with the real environment. We propose an algorithm for balancing the large number of samples from the high throughput but less accurate simulation and the low-throughput, high-fidelity and costly samples from the real environment. We achieve that by maintaining a replay buffer for each environment the agent interacts with. We analyze such multi-environment interaction theoretically, and provide convergence properties, through a novel theoretical replay buffer analysis. We demonstrate the efficacy of our method on a sim-to-real environment.

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 Bellmanconsistent 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 O(d) in its sample complexity when the action space is finite and small. Remarkably, our algorithms automatically adapt to the best bias-variance tradeoff in the hindsight, whereas most prior approaches require tuning extra hyperparameters a priori.

Recent progress in Quality Diversity Reinforcement Learning (QD-RL) has enabled learning a collection of behaviorally diverse, high performing policies. However, these methods typically involve storing thousands of policies, which results in high space-complexity and poor scaling to additional behaviors. Condensing the archive into a single model while retaining the performance and coverage of the original collection of policies has proved challenging. In this work, we propose using diffusion models to distill the archive into a single generative model over policy parameters. We show that our method achieves a compression ratio of 13x while recovering 98% of the original rewards and 89% of the original humanoid archive coverage. Further, the conditioning mechanism of diffusion models allows for flexibly selecting and sequencing behaviors, including using language.

De novo drug design is a pivotal issue in pharmacology and a new area of focus in AI for science research. A central challenge in this field is to generate molecules with specific properties while also producing a wide range of diverse candidates. Although advanced technologies such as transformer models and reinforcement learning have been applied in drug design, their potential has not been fully realized. Therefore, we propose MolRL-MGPT, a reinforcement learning algorithm with multiple GPT agents for drug molecular generation. To promote molecular diversity, we encourage the agents to collaborate in searching for desirable molecules in diverse directions. Our algorithm has shown promising results on the GuacaMol benchmark and exhibits efficacy in designing inhibitors against SARS-CoV-2 protein targets. The codes are available at: https://github.com/HXYfighter/