CIM: Constrained Intrinsic Motivation for Sparse-Reward Continuous Control

Intrinsic motivation is a promising exploration technique for solving reinforcement learning tasks with sparse or absent extrinsic rewards. There exist two technical challenges in implementing intrinsic motivation: 1) how to design a proper intrinsic objective to facilitate efficient exploration; and 2) how to combine the intrinsic objective with the extrinsic objective to help find better solutions. In the current literature, the intrinsic objectives are all designed in a task-agnostic manner and combined with the extrinsic objective via simple addition (or used by itself for reward-free pre-training). In this work, we show that these designs would fail in typical sparse-reward continuous control tasks. To address the problem, we propose Constrained Intrinsic Motivation (CIM) to leverage readily attainable task priors to construct a constrained intrinsic objective, and at the same time, exploit the Lagrangian method to adaptively balance the intrinsic and extrinsic objectives via a simultaneous-maximization framework. We empirically show, on multiple sparse-reward continuous control tasks, that our CIM approach achieves greatly improved performance and sample efficiency over state-of-the-art methods. Moreover, the key techniques of our CIM can also be plugged into existing methods to boost their performances

An adaptive nearest neighbor rule for classification

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may significantly vary between different points. (For example, the algorithm will use larger $k$ for predicting the labels of points in noisy regions.) We provide theory and experiments that demonstrate that the algorithm performs comparably to, and sometimes better than, $k$-NN with an optimal choice of $k$. In particular, we derive bounds on the convergence rates of our classifier that depend on a local quantity we call the `advantage' which is significantly weaker than the Lipschitz conditions used in previous convergence rate proofs. These generalization bounds hinge on a variant of the seminal Uniform Convergence Theorem due to Vapnik and Chervonenkis; this variant concerns conditional probabilities and may be of independent interest