Hazhar Rahmani

Hazhar Rahmani, Abhishek N. Kulkarni, Jie Fu · mila

In this paper, we study planning in stochastic systems, modeled as Markov decision processes (MDPs), with preferences over temporally extended goals. Prior work on temporal planning with preferences assumes that the user preferences form a total order, meaning that every pair of outcomes are comparable with each other. In this work, we consider the case where the preferences over possible outcomes are a partial order rather than a total order. We first introduce a variant of deterministic finite automaton, referred to as a preference DFA, for specifying the user's preferences over temporally extended goals. Based on the order theory, we translate the preference DFA to a preference relation over policies for probabilistic planning in a labeled MDP. In this treatment, a most preferred policy induces a weak-stochastic nondominated probability distribution over the finite paths in the MDP. The proposed planning algorithm hinges on the construction of a multi-objective MDP. We prove that a weak-stochastic nondominated policy given the preference specification is Pareto-optimal in the constructed multi-objective MDP, and vice versa. Throughout the paper, we employ a running example to demonstrate the proposed preference specification and solution approaches. We show the efficacy of our algorithm using the example with detailed analysis, and then discuss possible future directions.

Lening Li, Hazhar Rahmani, Jie Fu · mila

This paper studies temporal planning in probabilistic environments, modeled as labeled Markov decision processes (MDPs), with user preferences over multiple temporal goals. Existing works reflect such preferences as a prioritized list of goals. This paper introduces a new specification language, termed prioritized qualitative choice linear temporal logic on finite traces, which augments linear temporal logic on finite traces with prioritized conjunction and ordered disjunction from prioritized qualitative choice logic. This language allows for succinctly specifying temporal objectives with corresponding preferences accomplishing each temporal task. The finite traces that describe the system's behaviors are ranked based on their dissatisfaction scores with respect to the formula. We propose a systematic translation from the new language to a weighted deterministic finite automaton. Utilizing this computational model, we formulate and solve a problem of computing an optimal policy that minimizes the expected score of dissatisfaction given user preferences. We demonstrate the efficacy and applicability of the logic and the algorithm on several case studies with detailed analyses for each.

Hazhar Rahmani, Abhishek N. Kulkarni, Jie Fu

Human preferences are not always represented via complete linear orders: It is natural to employ partially-ordered preferences for expressing incomparable outcomes. In this work, we consider decision-making and probabilistic planning in stochastic systems modeled as Markov decision processes (MDPs), given a partially ordered preference over a set of temporally extended goals. Specifically, each temporally extended goal is expressed using a formula in Linear Temporal Logic on Finite Traces (LTL$_f$). To plan with the partially ordered preference, we introduce order theory to map a preference over temporal goals to a preference over policies for the MDP. Accordingly, a most preferred policy under a stochastic ordering induces a stochastic nondominated probability distribution over the finite paths in the MDP. To synthesize a most preferred policy, our technical approach includes two key steps. In the first step, we develop a procedure to transform a partially ordered preference over temporal goals into a computational model, called preference automaton, which is a semi-automaton with a partial order over acceptance conditions. In the second step, we prove that finding a most preferred policy is equivalent to computing a Pareto-optimal policy in a multi-objective MDP that is constructed from the original MDP, the preference automaton, and the chosen stochastic ordering relation. Throughout the paper, we employ running examples to illustrate the proposed preference specification and solution approaches. We demonstrate the efficacy of our algorithm using these examples, providing detailed analysis, and then discuss several potential future directions.

Hazhar Rahmani, Dylan A. Shell, Jason M. O'Kane

Suppose an agent asserts that it will move through an environment in some way. When the agent executes its motion, how does one verify the claim? The problem arises in a range of contexts including in validating safety claims about robot behavior, applications in security and surveillance, and for both the conception and the (physical) design and logistics of scientific experiments. Given a set of feasible sensors to select from, we ask how to choose sensors optimally in order to ensure that the agent's execution does indeed fit its pre-disclosed itinerary. Our treatment is distinguished from prior work in sensor selection by two aspects: the form the itinerary takes (a regular language of transitions) and that families of sensor choices can be grouped as a single choice. Both are intimately tied together, permitting construction of a product automaton because the same physical sensors (i.e., the same choice) can appear multiple times. This paper establishes the hardness of sensor selection for itinerary validation within this treatment, and proposes an exact algorithm based on an ILP formulation that is capable of solving problem instances of moderate size. We demonstrate its efficacy on small-scale case studies, including one motivated by wildlife tracking.

Yulin Zhang, Hazhar Rahmani, Dylan A. Shell et al.

Reduction of combinatorial filters involves compressing state representations that robots use. Such optimization arises in automating the construction of minimalist robots. But exact combinatorial filter reduction is an NP-complete problem and all current techniques are either inexact or formalized with exponentially many constraints. This paper proposes a new formalization needing only a polynomial number of constraints, and characterizes these constraints in three different forms: nonlinear, linear, and conjunctive normal form. Empirical results show that constraints in conjunctive normal form capture the problem most effectively, leading to a method that outperforms the others. Further examination indicates that a substantial proportion of constraints remain inactive during iterative filter reduction. To leverage this observation, we introduce just-in-time generation of such constraints, which yields improvements in efficiency and has the potential to minimize large filters.

Hazhar Rahmani, Jason M. O'Kane

In this paper, we consider a temporal logic planning problem in which the objective is to find an infinite trajectory that satisfies an optimal selection from a set of soft specifications expressed in linear temporal logic (LTL) while nevertheless satisfying a hard specification expressed in LTL. Our previous work considered a similar problem in which linear dynamic logic for finite traces (LDLf), rather than LTL, was used to express the soft constraints. In that work, LDLf was used to impose constraints on finite prefixes of the infinite trajectory. By using LTL, one is able not only to impose constraints on the finite prefixes of the trajectory, but also to set `soft' goals across the entirety of the infinite trajectory. Our algorithm first constructs a product automaton, on which the planning problem is reduced to computing a lasso with minimum cost. Among all such lassos, it is desirable to compute a shortest one. Though we prove that computing such a shortest lasso is computationally hard, we also introduce an efficient greedy approach to synthesize short lassos nonetheless. We present two case studies describing an implementation of this approach, and report results of our experiment comparing our greedy algorithm with an optimal baseline.