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This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be difficult to implement due to the potentially high computation complexity of the projection operation. In this paper, we relax the functional constraints by allowing them to be violated at each round but still requiring them to be satis ed in the long term. This type of relaxed online convex optimization (with long term constraints) was first considered in Mahdavi et al. (2012). That prior work proposes an algorithm to achieve O(sqrt(T)) regret and O(T^(3/4)) constraint violations for general problems and another algorithm to achieve an O(T^(2/3)) bound for both regret and constraint violations when the constraint set can be described by a nite number of linear constraints. A recent extension in Jenatton et al. (2016) can achieve O(T^(max(theta, 1-theta)) regret and O(T^(1-theta/2)) constraint violations where theta in (0,1). The current paper proposes a new simple algorithm that yields improved performance in comparison to prior works. The new algorithm achieves an O(sqrt(T)) regret bound with O(1) constraint violations.
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Trust the proc3s: Solving long-horizon robotics problems with llms and constraint satisfaction.
Recent developments in pretrained large language models (LLMs) ap- plied to robotics have demonstrated their capacity for sequencing a set of discrete skills to achieve open-ended goals in simple robotic tasks. In this paper, we ex- amine the topic of LLM planning for a set of continuously parameterized skills whose execution must avoid violations of a set of kinematic, geometric, and phys- ical constraints. We prompt the LLM to output code for a function with open parameters, which, together with environmental constraints, can be viewed as a Continuous Constraint Satisfaction Problem (CCSP). This CCSP can be solved through sampling or optimization to find a skill sequence and continuous param- eter settings that achieve the goal while avoiding constraint violations. Addition- ally, we consider cases where the LLM proposes unsatisfiable CCSPs, such as those that are kinematically infeasible, dynamically unstable, or lead to colli- sions, and re-prompt the LLM to form a new CCSP accordingly. Experiments across simulated and real-world domains demonstrate that our proposed strategy, PRoC3S, is capable of solving a wide range of complex manipulation tasks with realistic constraints much more efficiently and effectively than existing baselines.
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- Award ID(s):
- 2214177
- PAR ID:
- 10629482
- Publisher / Repository:
- Conference on Robot Learning
- Date Published:
- ISSN:
- 2640-3498
- Format(s):
- Medium: X
- Location:
- Munich, Germany
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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