Out-of-Distribution Optimality of Invariant Risk Minimization

• URL: http://arxiv.org/abs/2307.11972v1
• Date: Sat, 22 Jul 2023 03:31:15 GMT
• Title: Out-of-Distribution Optimality of Invariant Risk Minimization
• Authors: Shoji Toyota, Kenji Fukumizu
• Abstract summary: Invariant Risk Minimization (IRM) is considered to be a promising approach to minimize the o.o.d. risk. This paper rigorously proves that a solution to the bi-level optimization problem minimizes the o.o.d. risk under certain conditions.
• Score: 17.53032543377636
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Deep Neural Networks often inherit spurious correlations embedded in training data and hence may fail to generalize to unseen domains, which have different distributions from the domain to provide training data. M. Arjovsky et al. (2019) introduced the concept out-of-distribution (o.o.d.) risk, which is the maximum risk among all domains, and formulated the issue caused by spurious correlations as a minimization problem of the o.o.d. risk. Invariant Risk Minimization (IRM) is considered to be a promising approach to minimize the o.o.d. risk: IRM estimates a minimum of the o.o.d. risk by solving a bi-level optimization problem. While IRM has attracted considerable attention with empirical success, it comes with few theoretical guarantees. Especially, a solid theoretical guarantee that the bi-level optimization problem gives the minimum of the o.o.d. risk has not yet been established. Aiming at providing a theoretical justification for IRM, this paper rigorously proves that a solution to the bi-level optimization problem minimizes the o.o.d. risk under certain conditions. The result also provides sufficient conditions on distributions providing training data and on a dimension of feature space for the bi-leveled optimization problem to minimize the o.o.d. risk.

Related papers

• Pessimism Meets Risk: Risk-Sensitive Offline Reinforcement Learning [19.292214425524303]
  We study risk-sensitive reinforcement learning (RL), a crucial field due to its ability to enhance decision-making in scenarios where it is essential to manage uncertainty and minimize potential adverse outcomes. Our work focuses on applying the entropic risk measure to RL problems. We center on the linear Markov Decision Process (MDP) setting, a well-regarded theoretical framework that has yet to be examined from a risk-sensitive standpoint.
  arXiv  Detail & Related papers  (2024-07-10T13:09:52Z)
• Spectral-Risk Safe Reinforcement Learning with Convergence Guarantees [13.470544618339506]
  We propose a spectral risk measure-constrained RL algorithm, spectral-risk-constrained policy optimization (SRCPO) In the bilevel optimization structure, the outer problem involves optimizing dual variables derived from the risk measures, while the inner problem involves finding an optimal policy. The proposed method has been evaluated on continuous control tasks and showed the best performance among other RCRL algorithms satisfying the constraints.
  arXiv  Detail & Related papers  (2024-05-29T02:17:25Z)
• Robust Risk-Sensitive Reinforcement Learning with Conditional Value-at-Risk [23.63388546004777]
  We analyze the robustness of CVaR-based risk-sensitive RL under Robust Markov Decision Processes. Motivated by the existence of decision-dependent uncertainty in real-world problems, we study problems with state-action-dependent ambiguity sets.
  arXiv  Detail & Related papers  (2024-05-02T20:28:49Z)
• Risk-Sensitive RL with Optimized Certainty Equivalents via Reduction to Standard RL [48.1726560631463]
  We study Risk-Sensitive Reinforcement Learning with the Optimized Certainty Equivalent (OCE) risk. We propose two general meta-algorithms via reductions to standard RL. We show that it learns the optimal risk-sensitive policy while prior algorithms provably fail.
  arXiv  Detail & Related papers  (2024-03-10T21:45:12Z)
• Model-Based Epistemic Variance of Values for Risk-Aware Policy Optimization [59.758009422067]
  We consider the problem of quantifying uncertainty over expected cumulative rewards in model-based reinforcement learning. We propose a new uncertainty Bellman equation (UBE) whose solution converges to the true posterior variance over values. We introduce a general-purpose policy optimization algorithm, Q-Uncertainty Soft Actor-Critic (QU-SAC) that can be applied for either risk-seeking or risk-averse policy optimization.
  arXiv  Detail & Related papers  (2023-12-07T15:55:58Z)
• Domain Generalization without Excess Empirical Risk [83.26052467843725]
  A common approach is designing a data-driven surrogate penalty to capture generalization and minimize the empirical risk jointly with the penalty. We argue that a significant failure mode of this recipe is an excess risk due to an erroneous penalty or hardness in joint optimization. We present an approach that eliminates this problem. Instead of jointly minimizing empirical risk with the penalty, we minimize the penalty under the constraint of optimality of the empirical risk.
  arXiv  Detail & Related papers  (2023-08-30T08:46:46Z)
• Efficient Stochastic Approximation of Minimax Excess Risk Optimization [36.68685001551774]
  We develop efficient approximation approaches which directly target MERO. We demonstrate that the bias, caused by the estimation error of the minimal risk, is under-control. We also investigate a practical scenario where the quantity of samples drawn from each distribution may differ, and propose an approach that delivers distribution-dependent convergence rates.
  arXiv  Detail & Related papers  (2023-05-31T02:21:11Z)
• On the Variance, Admissibility, and Stability of Empirical Risk Minimization [80.26309576810844]
  Empirical Risk Minimization (ERM) with squared loss may attain minimax suboptimal error rates. We show that under mild assumptions, the suboptimality of ERM must be due to large bias rather than variance. We also show that our estimates imply stability of ERM, complementing the main result of Caponnetto and Rakhlin (2006) for non-Donsker classes.
  arXiv  Detail & Related papers  (2023-05-29T15:25:48Z)
• Efficient Risk-Averse Reinforcement Learning [79.61412643761034]
  In risk-averse reinforcement learning (RL), the goal is to optimize some risk measure of the returns. We prove that under certain conditions this inevitably leads to a local-optimum barrier, and propose a soft risk mechanism to bypass it. We demonstrate improved risk aversion in maze navigation, autonomous driving, and resource allocation benchmarks.
  arXiv  Detail & Related papers  (2022-05-10T19:40:52Z)
• Empirical Risk Minimization with Relative Entropy Regularization: Optimality and Sensitivity Analysis [7.953455469099826]
  The sensitivity of the expected empirical risk to deviations from the solution of the ERM-RER problem is studied. The expectation of the sensitivity is upper bounded, up to a constant factor, by the square root of the lautum information between the models and the datasets.
  arXiv  Detail & Related papers  (2022-02-09T10:55:14Z)
• The Risks of Invariant Risk Minimization [52.7137956951533]
  Invariant Risk Minimization is an objective based on the idea for learning deep, invariant features of data. We present the first analysis of classification under the IRM objective--as well as these recently proposed alternatives--under a fairly natural and general model. We show that IRM can fail catastrophically unless the test data are sufficiently similar to the training distribution--this is precisely the issue that it was intended to solve.
  arXiv  Detail & Related papers  (2020-10-12T14:54:32Z)

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.