风险建模

In this paper, we study risk-sensitive Reinforcement Learning (RL), focusing on the objective of Conditional Value at Risk (CVaR) with risk tolerance $\tau$. Starting with multi-arm bandits (MABs), we show the minimax CVaR regret rate is $\Omega(\sqrt{\tau^{-1}AK})$, where $A$ is the number of actions and $K$ is the number of episodes, and that it is achieved by an Upper Confidence Bound algorithm with a novel Bernstein bonus. For online RL in tabular Markov Decision Processes (MDPs), we show a minimax regret lower bound of $\Omega(\sqrt{\tau^{-1}SAK})$ (with normalized cumulative rewards), where $S$ is the number of states, and we propose a novel bonus-driven Value Iteration procedure. We show that our algorithm achieves the optimal regret of $\widetilde O(\sqrt{\tau^{-1}SAK})$ under a continuity assumption and in general attains a near-optimal regret of $\widetilde O(\tau^{-1}\sqrt{SAK})$, which is minimax-optimal for constant $\tau$. This improves on the best available bounds. By discretizing rewards appropriately, our algorithms are computationally efficient.

Risk-sensitive reinforcement learning (RL) has become a popular tool to control the risk of uncertain outcomes and ensure reliable performance in various sequential decision-making problems. While policy gradient methods have been developed for risk-sensitive RL, it remains unclear if these methods enjoy the same global convergence guarantees as in the risk-neutral case. In this paper, we consider a class of dynamic time-consistent risk measures, called Expected Conditional Risk Measures (ECRMs), and derive policy gradient updates for ECRM-based objective functions. Under both constrained direct parameterization and unconstrained softmax parameterization, we provide global convergence and iteration complexities of the corresponding risk-averse policy gradient algorithms. We further test risk-averse variants of REINFORCE and actor-critic algorithms to demonstrate the efficacy of our method and the importance of risk control.

In this paper, we study the problem of establishing the accountability and fairness of transparent machine learning models through monotonicity. Although there have been numerous studies on individual monotonicity, pairwise monotonicity is often overlooked in the existing literature. This paper studies transparent neural networks in the presence of three types of monotonicity: individual monotonicity, weak pairwise monotonicity, and strong pairwise monotonicity. As a means of achieving monotonicity while maintaining transparency, we propose the monotonic groves of neural additive models. As a result of empirical examples, we demonstrate that monotonicity is often violated in practice and that monotonic groves of neural additive models are transparent, accountable, and fair.

Self-supervised learning (SSL) is typically evaluated using a single metric (linear probing on ImageNet), which neither provides insight into tradeoffs between models nor highlights how to improve them. To address this, we propose an SSL risk decomposition, which generalizes the classical approximation-estimation decomposition. Our decomposition consists of four error terms: approximation, representation usability, probe generalization, and encoder generalization. We provide efficient estimators for each term and use them to analyze the effect of 30 design choices on 169 SSL vision models evaluated on ImageNet. Our analysis gives valuable insights for designing and using SSL models. For example, it highlights the main source of errors and shows how to improve SSL in specific settings (full- vs few-shot) by trading off error components.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

Based on the offset Rademacher complexity, this work outlines a systematical framework for deriving sharp excess risk bounds in statistical learning without Bernstein condition. In addition to recovering fast rates in a unified way for some parametric and nonparametric supervised learning models with minimum identifiability assumptions, we also obtain new and improved results for LAD (sparse) linear regression and deep logistic regression with deep ReLU neural networks, respectively.