Leveraging Hyperbolic Embeddings for Coarse-to-Fine Robot Design

Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these approaches often optimize robots directly in the vast design space, resulting in robots with complicated morphologies that are hard to control. In response, this paper presents a novel coarse-to-fine method for designing multi-cellular robots. Initially, this strategy seeks optimal coarse-grained robots and progressively refines them. To mitigate the challenge of determining the precise refinement juncture during the coarse-to-fine transition, we introduce the Hyperbolic Embeddings for Robot Design (HERD) framework. HERD unifies robots of various granularity within a shared hyperbolic space and leverages a refined Cross-Entropy Method for optimization. This framework enables our method to autonomously identify areas of exploration in hyperbolic space and concentrate on regions demonstrating promise. Finally, the extensive empirical studies on various challenging tasks sourced from EvoGym show our approach's superior efficiency and generalization capability.

Synthesizing Physically Plausible Human Motions in 3D Scenes

Synthesizing physically plausible human motions in 3D scenes is a challenging problem. Kinematics-based methods cannot avoid inherent artifacts (e.g., penetration and foot skating) due to the lack of physical constraints. Meanwhile, existing physics-based methods cannot generalize to multi-object scenarios since the policy trained with reinforcement learning has limited modeling capacity. In this work, we present a framework that enables physically simulated characters to perform long-term interaction tasks in diverse, cluttered, and unseen scenes. The key idea is to decompose human-scene interactions into two fundamental processes, Interacting and Navigating, which motivates us to construct two reusable Controller, i.e., InterCon and NavCon. Specifically, InterCon contains two complementary policies that enable characters to enter and leave the interacting state (e.g., sitting on a chair and getting up). To generate interaction with objects at different places, we further design NavCon, a trajectory following policy, to keep characters' locomotion in the free space of 3D scenes. Benefiting from the divide and conquer strategy, we can train the policies in simple environments and generalize to complex multi-object scenes. Experimental results demonstrate that our framework can synthesize physically plausible long-term human motions in complex 3D scenes. Code will be publicly released at https://github.com/liangpan99/InterScene.

Offline Meta Reinforcement Learning with In-Distribution Online Adaptation

Recent offline meta-reinforcement learning (meta-RL) methods typically utilize task-dependent behavior policies (e.g., training RL agents on each individual task) to collect a multi-task dataset. However, these methods always require extra information for fast adaptation, such as offline context for testing tasks. To address this problem, we first formally characterize a unique challenge in offline meta-RL: transition-reward distribution shift between offline datasets and online adaptation. Our theory finds that out-of-distribution adaptation episodes may lead to unreliable policy evaluation and that online adaptation with in-distribution episodes can ensure adaptation performance guarantee. Based on these theoretical insights, we propose a novel adaptation framework, called In-Distribution online Adaptation with uncertainty Quantification (IDAQ), which generates in-distribution context using a given uncertainty quantification and performs effective task belief inference to address new tasks. We find a return-based uncertainty quantification for IDAQ that performs effectively. Experiments show that IDAQ achieves state-of-the-art performance on the Meta-World ML1 benchmark compared to baselines with/without offline adaptation.

Symmetry-Aware Robot Design with Structured Subgroups

Robot design aims at learning to create robots that can be easily controlled and perform tasks efficiently. Previous works on robot design have proven its ability to generate robots for various tasks. However, these works searched the robots directly from the vast design space and ignored common structures, resulting in abnormal robots and poor performance. To tackle this problem, we propose a Symmetry-Aware Robot Design (SARD) framework that exploits the structure of the design space by incorporating symmetry searching into the robot design process. Specifically, we represent symmetries with the subgroups of the dihedral group and search for the optimal symmetry in structured subgroups. Then robots are designed under the searched symmetry. In this way, SARD can design efficient symmetric robots while covering the original design space, which is theoretically analyzed. We further empirically evaluate SARD on various tasks, and the results show its superior efficiency and generalizability.

Provably Efficient Gauss-Newton Temporal Difference Learning Method with Function Approximation

In this paper, based on the spirit of Fitted Q-Iteration (FQI), we propose a Gauss-Newton Temporal Difference (GNTD) method to solve the Q-value estimation problem with function approximation. In each iteration, unlike the original FQI that solves a nonlinear least square subproblem to fit the Q-iteration, the GNTD method can be viewed as an \emph{inexact} FQI that takes only one Gauss-Newton step to optimize this subproblem, which is much cheaper in computation. Compared to the popular Temporal Difference (TD) learning, which can be viewed as taking a single gradient descent step to FQI's subproblem per iteration, the Gauss-Newton step of GNTD better retains the structure of FQI and hence leads to better convergence. In our work, we derive the finite-sample non-asymptotic convergence of GNTD under linear, neural network, and general smooth function approximations. In particular, recent works on neural TD only guarantee a suboptimal $\mathcal{\mathcal{O}}(\epsilon^{-4})$ sample complexity, while GNTD obtains an improved complexity of $\tilde{\mathcal{O}}(\epsilon^{-2})$. Finally, we validate our method via extensive experiments in both online and offline RL problems. Our method exhibits both higher rewards and faster convergence than TD-type methods, including DQN.

A Near-Optimal Primal-Dual Method for Off-Policy Learning in CMDP

As an important framework for safe Reinforcement Learning, the Constrained Markov Decision Process (CMDP) has been extensively studied in the recent literature. However, despite the rich results under various on-policy learning settings, there still lacks some essential understanding of the offline CMDP problems, in terms of both the algorithm design and the information theoretic sample complexity lower bound. In this paper, we focus on solving the CMDP problems where only offline data are available. By adopting the concept of the single-policy concentrability coefficient $C^*$, we establish an $\Omega\left(\frac{\min\left\{|\mathcal{S}||\mathcal{A}|,|\mathcal{S}|+I\right\} C^*}{(1-\gamma)^3\epsilon^2}\right)$ sample complexity lower bound for the offline CMDP problem, where $I$ stands for the number of constraints. By introducing a simple but novel deviation control mechanism, we propose a near-optimal primal-dual learning algorithm called DPDL. This algorithm provably guarantees zero constraint violation and its sample complexity matches the above lower bound except for an $\tilde{\mathcal{O}}((1-\gamma)^{-1})$ factor. Comprehensive discussion on how to deal with the unknown constant $C^*$ and the potential asynchronous structure on the offline dataset are also included.

On the Sample Complexity and Metastability of Heavy-tailed Policy Search in Continuous Control

Reinforcement learning is a framework for interactive decision-making with incentives sequentially revealed across time without a system dynamics model. Due to its scaling to continuous spaces, we focus on policy search where one iteratively improves a parameterized policy with stochastic policy gradient (PG) updates. In tabular Markov Decision Problems (MDPs), under persistent exploration and suitable parameterization, global optimality may be obtained. By contrast, in continuous space, the non-convexity poses a pathological challenge as evidenced by existing convergence results being mostly limited to stationarity or arbitrary local extrema. To close this gap, we step towards persistent exploration in continuous space through policy parameterizations defined by distributions of heavier tails defined by tail-index parameter alpha, which increases the likelihood of jumping in state space. Doing so invalidates smoothness conditions of the score function common to PG. Thus, we establish how the convergence rate to stationarity depends on the policy's tail index alpha, a Holder continuity parameter, integrability conditions, and an exploration tolerance parameter introduced here for the first time. Further, we characterize the dependence of the set of local maxima on the tail index through an exit and transition time analysis of a suitably defined Markov chain, identifying that policies associated with Levy Processes of a heavier tail converge to wider peaks. This phenomenon yields improved stability to perturbations in supervised learning, which we corroborate also manifests in improved performance of policy search, especially when myopic and farsighted incentives are misaligned.

MARL with General Utilities via Decentralized Shadow Reward Actor-Critic

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $\epsilon$-stationarity in $\mathcal{O}(1/\epsilon^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/\epsilon^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.

On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method

Policy gradient gives rise to a rich class of reinforcement learning (RL) methods, for example the REINFORCE. Yet the best known sample complexity result for such methods to find an $\epsilon$-optimal policy is $\mathcal{O}(\epsilon^{-3})$, which is suboptimal. In this paper, we study the fundamental convergence properties and sample efficiency of first-order policy optimization method. We focus on a generalized variant of policy gradient method, which is able to maximize not only a cumulative sum of rewards but also a general utility function over a policy's long-term visiting distribution. By exploiting the problem's hidden convex nature and leveraging techniques from composition optimization, we propose a Stochastic Incremental Variance-Reduced Policy Gradient (SIVR-PG) approach that improves a sequence of policies to provably converge to the global optimal solution and finds an $\epsilon$-optimal policy using $\tilde{\mathcal{O}}(\epsilon^{-2})$ samples.

Variational Policy Gradient Method for Reinforcement Learning with General Utilities

In recent years, reinforcement learning (RL) systems with general goals beyond a cumulative sum of rewards have gained traction, such as in constrained problems, exploration, and acting upon prior experiences. In this paper, we consider policy optimization in Markov Decision Problems, where the objective is a general concave utility function of the state-action occupancy measure, which subsumes several of the aforementioned examples as special cases. Such generality invalidates the Bellman equation. As this means that dynamic programming no longer works, we focus on direct policy search. Analogously to the Policy Gradient Theorem \cite{sutton2000policy} available for RL with cumulative rewards, we derive a new Variational Policy Gradient Theorem for RL with general utilities, which establishes that the parametrized policy gradient may be obtained as the solution of a stochastic saddle point problem involving the Fenchel dual of the utility function. We develop a variational Monte Carlo gradient estimation algorithm to compute the policy gradient based on sample paths. We prove that the variational policy gradient scheme converges globally to the optimal policy for the general objective, though the optimization problem is nonconvex. We also establish its rate of convergence of the order $O(1/t)$ by exploiting the hidden convexity of the problem, and proves that it converges exponentially when the problem admits hidden strong convexity. Our analysis applies to the standard RL problem with cumulative rewards as a special case, in which case our result improves the available convergence rate.