Jongmin Lee

Jongmin Lee, Cihan Tepedelenlioglu, Andreas Spanias

A quantile is defined as a value below which random draws from a given distribution falls with a given probability. In a centralized setting where the cumulative distribution function (CDF) is unknown, the empirical CDF (ECDF) can be used to estimate such quantiles after aggregating the data. In a fully distributed sensor network, however, it is challenging to estimate quantiles. This is because each sensor node observes local measurement data with limited storage and data transmission power which make it difficult to obtain the global ECDF. This paper proposes consensus-based quantile estimation for such a distributed network. The states of the proposed algorithm are recursively updated with two-steps at each iteration: one is a local update based on the measurement data and the current state, and the other is averaging the updated states with neighboring nodes. We consider the realistic case of communication links between nodes being corrupted by independent random noise. It is shown that the estimated state sequence is asymptotically unbiased and converges toward the sample quantile in the mean-square sense. The two step-size sequences corresponding to the averaging and local update steps result in a mixed-time scale algorithm with proper decay rates in order to achieve convergence. We also provide applications to distributed estimation of trimmed mean, computation of median, maximum, or minimum values and identification of outliers through simulation.

Jongmin Lee, Meiqi Sun, Pieter Abbeel

In the unsupervised pre-training for reinforcement learning, the agent aims to learn a prior policy for downstream tasks without relying on task-specific reward functions. We focus on state entropy maximization (SEM), where the goal is to learn a policy that maximizes the entropy of the state stationary distribution. In this paper, we introduce SEMDICE, a principled off-policy algorithm that computes an SEM policy from an arbitrary off-policy dataset, which optimizes the policy directly within the space of stationary distributions. SEMDICE computes a single, stationary Markov state-entropy-maximizing policy from an arbitrary off-policy dataset. Experimental results demonstrate that SEMDICE outperforms baseline algorithms in maximizing state entropy while achieving the best adaptation efficiency for downstream tasks among SEM-based unsupervised RL pre-training methods.

Jongmin Lee, Ernest K. Ryu

Although there is an extensive body of work characterizing the sample complexity of discounted-return offline RL with function approximations, prior work on the average-reward setting has received significantly less attention, and existing approaches rely on restrictive assumptions, such as ergodicity or linearity of the MDP. In this work, we establish the first sample complexity results for average-reward offline RL with function approximation for weakly communicating MDPs, a much milder assumption. To this end, we introduce Anchored Fitted Q-Iteration, which combines the standard Fitted Q-Iteration with an anchor mechanism. We show that the anchor, which can be interpreted as a form of weight decay, is crucial for enabling finite-time analysis in the average-reward setting. We also extend our finite-time analysis to the setup where the dataset is generated from a single-trajectory rather than IID transitions, again leveraging the anchor mechanism.