In this section, we provide a convergence rate analysis for Algorithm 1. Similar to Hazan et al. [36], Algorithm 1 has access to an approximate density oracle and an approximate planner defined below: Visitation density oracle: We assume access to an approximate density estimator that takes in a policy and a density approximation error d 0 as inputs and returns ˆd such that kd ˆd k1 d. Approximate planning oracle: We assume access to an approximate planner that, given any MDP M and error tolerance p 0, returns a policy such that JM() max JM() p. A.1 Proof of Theorem 1 We first give the following proposition that captures certain properties of the proposed objective. The proof is postponed to the end of this section. Taking the above proposition as given for the moment, we prove Theorem 1 following steps similar to those of Hazan et al. [36, Theorem 4.1]. Since k returned by the approximate planning oracle is an p-optimal policy in Mk, we have (1) 1hd k,rki (1) 1hd,rki p for any policy, including?. Therefore, It is straightforward to check that setting 0.1 1, p 0.1, d 0.1 1, 0.1, and the number of iterations K 1 log(10B 1) yields the claim of Theorem 1. Remark 2. Since the temperature parameter k in Proposition 1 goes to zero as k increases, one can show that the expected value of policy returned by Algorithm 1 converges to the maximum performance J(?).

We provide final testing performance for NovelD and all baselines in MiniGrid. We also provide more intrinsic analysis similar to Sec. 4.2 in a seven-room environment in Figure 1. There are other categories of static environment. The initial position of the agent and goal can be random. The position of the agent and goal is randomized.

Abstract-- Robotic systems, particularly in demanding environments like narrow corridors or disaster zones, often grapple with imperfect state estimation. Addressing this challenge requires a trajectory plan that not only navigates these restrictive spaces but also manages the inherent uncertainty of the system. We present a novel approach for graph-based belief space planning via the use of an efficient covariance control algorithm. By adaptively steering state statistics via output state feedback, we efficiently craft a belief roadmap characterized by nodes with controlled uncertainty and edges representing collision-free mean trajectories. The roadmap's structured design then paves the way for precise path searches that balance control costs and uncertainty considerations. Figure 1: A belief space graph depicting sampled state beliefs I.

We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory distribution by a tractable Gaussian distribution. Equivalently, the proposed framework can be viewed as a standard motion planning with an entropy regularization. Thus, the solution obtained is a transition from an optimal deterministic solution to a stochastic one, and the proposed framework can recover the deterministic solution by controlling the level of stochasticity. To solve this optimization, we adopt the natural gradient descent scheme. The sparsity structure of the proposed formulation induced by factorized objective functions is further leveraged to improve the scalability of the algorithm. We evaluate our method on several robot systems in simulated environments, and show that it achieves collision avoidance with smooth trajectories, and meanwhile brings robustness to the deterministic baseline results, especially in challenging environments and tasks.

A key challenge for reinforcement learning (RL) consists of learning in environments with sparse extrinsic rewards. In contrast to current RL methods, humans are able to learn new skills with little or no reward by using various forms of intrinsic motivation. We propose AMIGo, a novel agent incorporating a goal-generating teacher that proposes Adversarially Motivated Intrinsic Goals to train a goal-conditioned "student" policy in the absence of (or alongside) environment reward. Specifically, through a simple but effective "constructively adversarial" objective, the teacher learns to propose increasingly challenging---yet achievable---goals that allow the student to learn general skills for acting in a new environment, independent of the task to be solved. We show that our method generates a natural curriculum of self-proposed goals which ultimately allows the agent to solve challenging procedurally-generated tasks where other forms of intrinsic motivation and state-of-the-art RL methods fail.