Learning Submodular Objectives for Team Environmental Monitoring

Wilde, Nils; Sadeghi, Armin; Smith, Stephen L.

doi:10.1109/lra.2021.3135928

“…Future work should also consider HRI frameworks that help users to select the policy that best fits their preferences. One approach could be choice-based learning where the user iteratively chooses between two presented options [5], [19], [54], [55]. Adapting this to MO-MRPD should explore how the variance of MRPD policies affect human choices, i.e., how humans can choose between different policies when their cost distributions are similar.…”

Section: Discussion and Future Workmentioning

confidence: 99%

“…Many robotic planning problems face the challenge of being required to simultaneously optimize multiple objectives, for instance in path and trajectory planning [5], [8], [10], autonomous driving [11]- [14] transportation and mobility on demand [3], multi-robot planning [15]- [19].…”

Section: B Related Workmentioning

confidence: 99%

“…b) User preferences for competing objectives: Researchers in human-robot interaction (HRI) study the problem of reward learning which seeks to interactively learn a reward or cost function that best describes a user's preference for robot behaviour [51]. Usually, this reward function is modelled as a weighted sum of features [5], [19], [52]- [55], which is equivalent to the linear scalarization of a MOO problem. Thus, learning a user's reward function is equivalent to finding the Pareto-optimal trade-off that best fit their preferences.…”

Section: B Related Workmentioning

confidence: 99%

“…Given the robot types, let F be a multi-set containing ⌈ B /bi⌉ robots of each type R i . By construction, any feasible solution to (1) is a subset of F. This allows us to treat the problem as a heterogeneous variant of the team orienteering problem (TOP) [27], [28] with robots F where only some robots execute a tour of non-zero length, i.e. activated.…”

Section: A Approachmentioning

confidence: 99%

See 2 more Smart Citations

Online Multi-Robot Task Assignment with Stochastic Blockages

Wilde

¹

,

Alonso–Mora

²

2022

2022 IEEE 61st Conference on Decision and Control (CDC)

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0

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We study the problem of finding statistically distinct plans for stochastic planning and task assignment problems such as online multi-robot pickup and delivery (MRPD) when facing multiple competing objectives. In many real-world settings robot fleets do not only need to fulfil delivery requests, but also have to consider auxiliary objectives such as energy efficiency or avoiding human-centered work spaces. We pose MRPD as a multiobjective optimization problem where the goal is to find MRPD policies that yield different trade-offs between given objectives. There are two main challenges: 1) MRPD is computationally hard, which limits the number of trade-offs that can reasonably be computed, and 2) due to the random task arrivals, one needs to consider statistical variance of the objective values in addition to the average. We present an adaptive sampling algorithm that finds a set of policies which i) are approximately optimal, ii) approximate the set of all optimal solutions, and iii) are statistically distinguishable. We prove completeness and adapt a state-of-the-art MRPD solver to the multi-objective setting for three example objectives. In a series of simulation experiments we demonstrate the advantages of the proposed method compared to baseline approaches and show its robustness in a sensitivity analysis. The approach is general and could be adapted to other multi-objective task assignment and planning problems under uncertainty.

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“…In this work, we propose a method to compute a finite set of weights Ω ⊂ W that will, for any w * ∈ W, allow us to approximate u(w * ) with u(w ) for an appropriately chosen w ∈ Ω. To evaluate the quality of a candidate set Ω, we use the notion of regret from [11,26], defined formally here: Definition 1 (Regret). Given two weights w , w * ∈ W, the regret of w under w * is defined as…”

Section: Problem Statementmentioning

confidence: 99%

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Botros¹,

Sadeghi²,

Wilde³

et al. 2022

Preprint

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0

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Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the original multi-objective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Using uniformly spaced weight vectors is often inefficient and does not provide error bounds. Thus, we address the problem of computing a finite set of weight vectors such that for any other weight vector, there exists an element in the set whose error compared to optimal is minimized. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector, including its continuity and concavity. Using these, we propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the error. Finally, we illustrate that the proposed approach significantly outperforms uniformly distributed weights for different robot planning problems with varying numbers of objective functions.

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Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Botros

¹

,

Sadeghi²,

Wilde³

et al. 2022

Springer Proceedings in Advanced Robotics

Self Cite

View full text Add to dashboard Cite

Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the original multi-objective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Using uniformly spaced weight vectors is often inefficient and does not provide error bounds. Thus, we address the problem of computing a finite set of weight vectors such that for any other weight vector, there exists an element in the set whose error compared to optimal is minimized. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector, including its continuity and concavity. Using these, we propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the error. Finally, we illustrate that the proposed approach significantly outperforms uniformly distributed weights for different robot planning problems with varying numbers of objective functions.

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Learning Submodular Objectives for Team Environmental Monitoring

Cited by 13 publications

References 24 publications

Online Multi-Robot Task Assignment with Stochastic Blockages

Online Multi-Robot Task Assignment with Stochastic Blockages

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems

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