Alperen Tercan

Alperen Tercan, Vinayak S. Prabhu

Lexicographic multi-objective problems, which impose a lexicographic importance order over the objectives, arise in many real-life scenarios. Existing Reinforcement Learning work directly addressing lexicographic tasks has been scarce. The few proposed approaches were all noted to be heuristics without theoretical guarantees as the Bellman equation is not applicable to them. Additionally, the practical applicability of these prior approaches also suffers from various issues such as not being able to reach the goal state. While some of these issues have been known before, in this work we investigate further shortcomings, and propose fixes for improving practical performance in many cases. We also present a policy optimization approach using our Lexicographic Projection Optimization (LPO) algorithm that has the potential to address these theoretical and practical concerns. Finally, we demonstrate our proposed algorithms on benchmark problems.

Alperen Tercan, Necmiye Ozay

Constrained Markov Decision Processes (CMDPs) are notably more complex to solve than standard MDPs due to the absence of universally optimal policies across all initial state distributions. This necessitates re-solving the CMDP whenever the initial distribution changes. In this work, we analyze how the optimal value of CMDPs varies with different initial distributions, deriving bounds on these variations using duality analysis of CMDPs and perturbation analysis in linear programming. Moreover, we show how such bounds can be used to analyze the regret of a given policy due to unknown variations of the initial distribution.

Mohamad Louai Shehab, Alperen Tercan, Necmiye Ozay

In this paper, we consider the problem of recovering time-varying reward functions from either optimal policies or demonstrations coming from a max entropy reinforcement learning problem. This problem is highly ill-posed without additional assumptions on the underlying rewards. However, in many applications, the rewards are indeed parsimonious, and some prior information is available. We consider two such priors on the rewards: 1) rewards are mostly constant and they change infrequently, 2) rewards can be represented by a linear combination of a small number of feature functions. We first show that the reward identification problem with the former prior can be recast as a sparsification problem subject to linear constraints. Moreover, we give a polynomial-time algorithm that solves this sparsification problem exactly. Then, we show that identifying rewards representable with the minimum number of features can be recast as a rank minimization problem subject to linear constraints, for which convex relaxations of rank can be invoked. In both cases, these observations lead to efficient optimization-based reward identification algorithms. Several examples are given to demonstrate the accuracy of the recovered rewards as well as their generalizability.