The goal location is small region around (20,20). In each task, S0 was a set of arm con gurations establishing contact with the 539 end-effector, the 6-DoF change in stiffness, and 1-DoF gripper state. The fraction of start states in S0 that lead to success 557 IVF, classi er). The result of that execution is recorded as 552 Algorithm 1 is the pseudocode used for the experiments described in Section 4.1. Episodes last a maximum of 1000 steps.

We first verify the statement for the terminal state f. Observe that at the terminal state f, regardless of the action taken, the next state is always f and the reward is always 0. Hence Q h(f,) = V h(f) = 0 for all h [H]. Thus Q h(f,) = hφ(f,),v(a)i= 0. We now verify realizability for other states via induction on h = H,H 1,,1. Next, note that h, (2) follows from (1). In other words, (1) implies that a is always the optimal action.

Synchronizing decisions across multiple agents in realistic settings is problematic since it requires agents to wait for other agents to terminate and communicate about termination reliably. Ideally, agents should learn and execute asynchronously instead. Such asynchronous methods also allow temporally extended actions that can take different amounts of time based on the situation and action executed. Unfortunately, current policy gradient methods are not applicable in asynchronous settings, as they assume that agents synchronously reason about action selection at every time step. To allow asynchronous learning and decision-making, we formulate a set of asynchronous multi-agent actor-critic methods that allow agents to directly optimize asynchronous policies in three standard training paradigms: decentralized learning, centralized learning, and centralized training for decentralized execution. Empirical results (in simulation and hardware) in a variety of realistic domains demonstrate the superiority of our approaches in large multi-agent problems and validate the effectiveness of our algorithms for learning high-quality and asynchronous solutions.

Long-horizon robotic manipulation tasks typically involve a series of interrelated sub-tasks spanning multiple execution stages. Skill chaining offers a feasible solution for these tasks by pre-training the skills for each sub-task and linking them sequentially. However, imperfections in skill learning or disturbances during execution can lead to the accumulation of errors in skill chaining process, resulting in execution failures. In this paper, we investigate how to achieve stable and smooth skill chaining for long-horizon robotic manipulation tasks. Specifically, we propose a novel skill chaining framework called Skill Chaining via Dual Regularization (SCaR). This framework applies dual regularization to sub-task skill pre-training and fine-tuning, which not only enhances the intra-skill dependencies within each sub-task skill but also reinforces the inter-skill dependencies between sequential sub-task skills, thus ensuring smooth skill chaining and stable long-horizon execution. We evaluate the SCaR framework on two representative long-horizon robotic manipulation simulation benchmarks: IKEA furniture assembly and kitchen organization. Additionally, we conduct a simple real-world validation in tabletop robot pick-and-place tasks. The experimental results show that, with the support of SCaR, the robot achieves a higher success rate in long-horizon tasks compared to relevant baselines and demonstrates greater robustness to perturbations.