Statistical Learning with Conditional Value at Risk

• URL: http://arxiv.org/abs/2002.05826v1
• Date: Fri, 14 Feb 2020 00:58:34 GMT
• Title: Statistical Learning with Conditional Value at Risk
• Authors: Tasuku Soma and Yuichi Yoshida
• Abstract summary: We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss.
• Score: 35.4968603057034
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a risk-averse statistical learning framework wherein the performance of a learning algorithm is evaluated by the conditional value-at-risk (CVaR) of losses rather than the expected loss. We devise algorithms based on stochastic gradient descent for this framework. While existing studies of CVaR optimization require direct access to the underlying distribution, our algorithms make a weaker assumption that only i.i.d.\ samples are given. For convex and Lipschitz loss functions, we show that our algorithm has $O(1/\sqrt{n})$-convergence to the optimal CVaR, where $n$ is the number of samples. For nonconvex and smooth loss functions, we show a generalization bound on CVaR. By conducting numerical experiments on various machine learning tasks, we demonstrate that our algorithms effectively minimize CVaR compared with other baseline algorithms.

Related papers

• SOREL: A Stochastic Algorithm for Spectral Risks Minimization [1.6574413179773761]
  spectral risk has wide applications in machine learning, especially in real-world decision-making. By assigning different weights to the losses of different sample points, it allows the model's performance to lie between the average performance and the worst-case performance. We propose SOREL, the first gradient-based algorithm with convergence guarantees for the spectral risk minimization.
  arXiv  Detail & Related papers  (2024-07-19T18:20:53Z)
• Provably Efficient CVaR RL in Low-rank MDPs [58.58570425202862]
  We study risk-sensitive Reinforcement Learning (RL) We propose a novel Upper Confidence Bound (UCB) bonus-driven algorithm to balance interplay between exploration, exploitation, and representation learning in CVaR RL. We prove that our algorithm achieves a sample complexity of $epsilon$-optimal CVaR, where $H$ is the length of each episode, $A$ is the capacity of action space, and $d$ is the dimension of representations.
  arXiv  Detail & Related papers  (2023-11-20T17:44:40Z)
• Forward-PECVaR Algorithm: Exact Evaluation for CVaR SSPs [1.347733333991357]
  Conditional Value at Risk (CVaR) is a criterion that allows modeling an arbitrary level of risk. We propose a new algorithm, Forward-PECVaR, that evaluates exactly stationary policies of CVaR-SSPs with non-uniform costs.
  arXiv  Detail & Related papers  (2023-03-01T17:10:22Z)
• Improved Regret for Efficient Online Reinforcement Learning with Linear Function Approximation [69.0695698566235]
  We study reinforcement learning with linear function approximation and adversarially changing cost functions. We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback.
  arXiv  Detail & Related papers  (2023-01-30T17:26:39Z)
• Boosted CVaR Classification [44.731468512484824]
  A popular approach to maximize the model's tail performance is to minimize the CVaR loss. We show that for classification tasks where models are evaluated by the zero-one loss, the minimizer of the average zero-one loss also minimizes the CVaR zero-one loss. We propose the Boosted CVaR Classification framework which is motivated by a direct relationship between CVaR and a classical boosting algorithm called LPBoost.
  arXiv  Detail & Related papers  (2021-10-26T18:27:25Z)
• Randomized Exploration for Reinforcement Learning with General Value Function Approximation [122.70803181751135]
  We propose a model-free reinforcement learning algorithm inspired by the popular randomized least squares value iteration (RLSVI) algorithm. Our algorithm drives exploration by simply perturbing the training data with judiciously chosen i.i.d. scalar noises. We complement the theory with an empirical evaluation across known difficult exploration tasks.
  arXiv  Detail & Related papers  (2021-06-15T02:23:07Z)
• Risk Minimization from Adaptively Collected Data: Guarantees for Supervised and Policy Learning [57.88785630755165]
  Empirical risk minimization (ERM) is the workhorse of machine learning, but its model-agnostic guarantees can fail when we use adaptively collected data. We study a generic importance sampling weighted ERM algorithm for using adaptively collected data to minimize the average of a loss function over a hypothesis class. For policy learning, we provide rate-optimal regret guarantees that close an open gap in the existing literature whenever exploration decays to zero.
  arXiv  Detail & Related papers  (2021-06-03T09:50:13Z)
• Noisy Linear Convergence of Stochastic Gradient Descent for CV@R Statistical Learning under Polyak-{\L}ojasiewicz Conditions [4.721069729610892]
  Conditional Value-at-Risk ($mathrmCV@R$) is one of the most popular measures of risk. We prove that $mathrmCV@R$ can be used as a performance criterion in supervised statistical learning.
  arXiv  Detail & Related papers  (2020-12-14T18:22:53Z)
• Stochastic Hard Thresholding Algorithms for AUC Maximization [49.00683387735522]
  We develop a hard thresholding algorithm for AUC in distributiond classification. We conduct experiments to show the efficiency and effectiveness of the proposed algorithms.
  arXiv  Detail & Related papers  (2020-11-04T16:49:29Z)
• Large-Scale Methods for Distributionally Robust Optimization [53.98643772533416]
  We prove that our algorithms require a number of evaluations gradient independent of training set size and number of parameters. Experiments on MNIST and ImageNet confirm the theoretical scaling of our algorithms, which are 9--36 times more efficient than full-batch methods.
  arXiv  Detail & Related papers  (2020-10-12T17:41:44Z)
• Learning with CVaR-based feedback under potentially heavy tails [8.572654816871873]
  We study learning algorithms that seek to minimize the conditional value-at-risk (CVaR) We first study a general-purpose estimator of CVaR for potentially heavy-tailed random variables. We then derive a new learning algorithm which robustly chooses among candidates produced by gradient-driven sub-processes.
  arXiv  Detail & Related papers  (2020-06-03T01:08:29Z)

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.