Stochastic Compositional Optimization with Compositional Constraints

• URL: http://arxiv.org/abs/2209.04086v1
• Date: Fri, 9 Sep 2022 02:06:35 GMT
• Title: Stochastic Compositional Optimization with Compositional Constraints
• Authors: Shuoguang Yang, Zhe Zhang, Ethan X. Fang
• Abstract summary: We study a novel model that incorporates single-level expected value and two-level compositional constraints into the current SCO framework. Our model can be applied widely to data-driven optimization and risk management, including risk-averse optimization and high-moment portfolio selection. We propose a class of primal-dual algorithms that generates sequences converging to the optimal solution at the rate of $cO(frac1sqrtN)$under both single-level expected value and two-level compositional constraints.
• Score: 8.535822787583486
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic compositional optimization (SCO) has attracted considerable attention because of its broad applicability to important real-world problems. However, existing works on SCO assume that the projection within a solution update is simple, which fails to hold for problem instances where the constraints are in the form of expectations, such as empirical conditional value-at-risk constraints. We study a novel model that incorporates single-level expected value and two-level compositional constraints into the current SCO framework. Our model can be applied widely to data-driven optimization and risk management, including risk-averse optimization and high-moment portfolio selection, and can handle multiple constraints. We further propose a class of primal-dual algorithms that generates sequences converging to the optimal solution at the rate of $\cO(\frac{1}{\sqrt{N}})$under both single-level expected value and two-level compositional constraints, where $N$ is the iteration counter, establishing the benchmarks in expected value constrained SCO.

Related papers

• Double Duality: Variational Primal-Dual Policy Optimization for Constrained Reinforcement Learning [132.7040981721302]
  We study the Constrained Convex Decision Process (MDP), where the goal is to minimize a convex functional of the visitation measure. Design algorithms for a constrained convex MDP faces several challenges, including handling the large state space.
  arXiv  Detail & Related papers  (2024-02-16T16:35:18Z)
• Algorithm for Constrained Markov Decision Process with Linear Convergence [55.41644538483948]
  An agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its costs. A new dual approach is proposed with the integration of two ingredients: entropy regularized policy and Vaidya's dual. The proposed approach is shown to converge (with linear rate) to the global optimum.
  arXiv  Detail & Related papers  (2022-06-03T16:26:38Z)
• Comparing Classical-Quantum Portfolio Optimization with Enhanced Constraints [0.0]
  We show how to add fundamental analysis to the portfolio optimization problem, adding in asset-specific and global constraints based on chosen balance sheet metrics. We analyze the current state-of-the-art algorithms for solving such a problem using D-Wave's Quantum Processor and compare the quality of the solutions obtained to commercially-available optimization software.
  arXiv  Detail & Related papers  (2022-03-09T17:46:32Z)
• Online Learning with Knapsacks: the Best of Both Worlds [54.28273783164608]
  We casting online learning problems in which a decision maker wants to maximize their expected reward without violating a finite set of $m$m resource constraints. Our framework allows the decision maker to handle its evidence flexibility and costoretic functions.
  arXiv  Detail & Related papers  (2022-02-28T12:10:48Z)
• A Globally Convergent Evolutionary Strategy for Stochastic Constrained Optimization with Applications to Reinforcement Learning [0.6445605125467573]
  Evolutionary strategies have been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. Convergence guarantees for evolutionary strategies to optimize constrained problems are however lacking in the literature.
  arXiv  Detail & Related papers  (2022-02-21T17:04:51Z)
• Faster Algorithm and Sharper Analysis for Constrained Markov Decision Process [56.55075925645864]
  The problem of constrained decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints. A new utilities-dual convex approach is proposed with novel integration of three ingredients: regularized policy, dual regularizer, and Nesterov's gradient descent dual. This is the first demonstration that nonconcave CMDP problems can attain the lower bound of $mathcal O (1/epsilon)$ for all complexity optimization subject to convex constraints.
  arXiv  Detail & Related papers  (2021-10-20T02:57:21Z)
• Momentum Accelerates the Convergence of Stochastic AUPRC Maximization [80.8226518642952]
  We study optimization of areas under precision-recall curves (AUPRC), which is widely used for imbalanced tasks. We develop novel momentum methods with a better iteration of $O (1/epsilon4)$ for finding an $epsilon$stationary solution. We also design a novel family of adaptive methods with the same complexity of $O (1/epsilon4)$, which enjoy faster convergence in practice.
  arXiv  Detail & Related papers  (2021-07-02T16:21:52Z)
• A Lyapunov-Based Methodology for Constrained Optimization with Bandit Feedback [22.17503016665027]
  We consider problems where each action returns a random reward, cost, and penalty from an unknown joint distribution. We propose a novel low-complexity algorithm, named $tt LyOn$, and prove that it achieves $O(sqrtBlog B)$ regret and $O(log B/B)$ constraint-violation. The low computational cost bounds of $tt LyOn$ suggest that Lyapunov-based algorithm design methodology can be effective in solving constrained bandit optimization problems.
  arXiv  Detail & Related papers  (2021-06-09T16:12:07Z)
• Modeling the Second Player in Distributionally Robust Optimization [90.25995710696425]
  We argue for the use of neural generative models to characterize the worst-case distribution. This approach poses a number of implementation and optimization challenges. We find that the proposed approach yields models that are more robust than comparable baselines.
  arXiv  Detail & Related papers  (2021-03-18T14:26:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.