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Delegated portfolio management with random default

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arXiv 2024年

作者： Gennaro, Alberto Mastrolia, Thibaut Department of Industrial Engineering and Operations Research UC Berkeley United States

We are considering the problem of optimal portfolio delegation between an investor and a portfolio manager under a random default time. We focus on a novel variation of the Principal-Agent problem adapted to this framework. We address the challenge of an uncertain investment horizon caused by an exogenous random default time, after which neither the agent nor the principal can access the market. This uncertainty introduces significant complexities in analyzing the problem, requiring distinct mathematical approaches for two cases: when the random default time falls within the initial time frame [0,T] and when it extends beyond this period. We develop a theoretical framework to model the stochastic dynamics of the investment process, incorporating the random default time. We then analyze the portfolio manager’s investment decisions and compensation mechanisms for both scenarios. In the first case, where the default time could be unbounded, we apply traditional results from Backward Stochastic Differential Equations (BSDEs) and control theory to address the agent problem. In the second case, where the default time is within the interval [0,T], the problem becomes more intricate due to the degeneracy of the BSDE’s driver. For both scenarios, we demonstrate that the contracting problem can be resolved by examining the existence of solutions to integro-partial Hamilton-Jacobi-Bellman (HJB) equations in both situations. We develop a deep-learning algorithm to solve the problem in high-dimension with no access to the optimizer of the Hamiltonian function. © 2024, CC BY.

关键词： Stochastic systems

Statistical Inference and A/B Testing in Fisher Markets and Paced Auctions

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arXiv 2024年

作者： Liao, Luofeng Kroer, Christian Department of Industrial Engineering and Operations Research Columbia University United States

We initiate the study of statistical inference and A/B testing for two market equilibrium models: linear Fisher market (LFM) equilibrium and first-price pacing equilibrium (FPPE). LFM arises from fair resource allocation systems such as allocation of food to food banks. For LFM, we assume that the observed data is captured by the classical finite-dimensional Fisher market equilibrium, and its steady-state behavior is modeled by a continuous limit Fisher market. The FPPE model arises from internet advertising where advertisers are constrained by budgets and advertising opportunities are sold via first-price auctions. We propose a statistical framework for the FPPE model, in which a continuous limit FPPE models the steady-state behavior of the auction platform, and a finite FPPE provides the data to estimate primitives of the limit FPPE. Both LFM and FPPE have an Eisenberg-Gale convex program characterization, the pillar upon which we derive our statistical theory. We start by deriving basic convergence results for the finite market to the limit market. We then derive asymptotic distributions, and construct confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of estimation based on finite markets. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Synthetic and semi-synthetic experiments verify the validity and practicality of our theory. © 2024, CC BY.

关键词： Statistical tests

Energy-Efficient Scheduling with Predictions

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arXiv 2024年

作者： Balkanski, Eric Perivier, Noemie Stein, Clifford Wei, Hao-Ting Department of Industrial Engineering and Operations Research Columbia University United States

An important goal of modern scheduling systems is to efficiently manage power usage. In energy-efficient scheduling, the operating system controls the speed at which a machine is processing jobs with the dual objective of minimizing energy consumption and optimizing the quality of service cost of the resulting schedule. Since machine-learned predictions about future requests can often be learned from historical data, a recent line of work on learning-augmented algorithms aims to achieve improved performance guarantees by leveraging predictions. In particular, for energy-efficient scheduling, Bamas et al. [7] and Antoniadis et al. [4] designed algorithms with predictions for the energy minimization with deadlines problem and achieved an improved competitive ratio when the prediction error is small while also maintaining worst-case bounds even when the prediction error is arbitrarily large. In this paper, we consider a general setting for energy-efficient scheduling and provide a flexible learning-augmented algorithmic framework that takes as input an offline and an online algorithm for the desired energy-efficient scheduling problem. We show that, when the prediction error is small, this framework gives improved competitive ratios for many different energy-efficient scheduling problems, including energy minimization with deadlines, while also maintaining a bounded competitive ratio regardless of the prediction error. Finally, we empirically demonstrate that this framework achieves an improved performance on real and synthetic datasets. Copyright © 2024, The Authors. All rights reserved.

关键词： Forecasting

How Does Goal Relabeling Improve Sample Efficiency? 41

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How Does Goal Relabeling Improve Sample Efficiency?

41st International Conference on Machine Learning, ICML 2024

作者： Zheng, Sirui Bai, Chenjia Yang, Zhuoran Wang, Zhaoran Department of Industrial Engineering and Management Sciences Northwestern University EvanstonIL60208 United States Shanghai Artificial Intelligence Laboratory China Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08544 United States

Hindsight experience replay and goal relabeling are successful in reinforcement learning (RL) since they enable agents to learn from *** their successes, we lack a theoretical understanding, such as (i) why hindsight experience replay improves sample efficiency and (ii) how to design a relabeling method that achieves sample *** this end, we construct an example to show the information-theoretical improvement in sample efficiency achieved by goal *** example reveals that goal relabeling can enhance sample efficiency and exploit the rich information in observations through better hypothesis *** on these insights, we develop an RL algorithm called *** analyze the sample complexity of GOALIVE, we introduce a complexity measure, the goal-conditioned Bellman-Eluder (GOAL-BE) dimension, which characterizes the sample complexity of goal-conditioned RL *** to the Bellman-Eluder dimension, the goal-conditioned version offers an exponential improvement in the best *** the best of our knowledge, our work provides the first characterization of the theoretical improvement in sample efficiency achieved by goal relabeling. Copyright 2024 by the author(s)

关键词： Reinforcement learning

Is Cross-Validation the Gold Standard to Evaluate Model Performance?

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arXiv 2024年

作者： Iyengar, Garud Lam, Henry Wang, Tianyu Department of Industrial Engineering and Operations Research Columbia University United States

Cross-Validation (CV) is the default choice for evaluating the performance of machine learning models. Despite its wide usage, their statistical benefits have remained half-understood, especially in challenging nonparametric regimes. In this paper we fill in this gap and show that in fact, for a wide spectrum of models, CV does not statistically outperform the simple "plug-in" approach where one reuses training data for testing evaluation. Specifically, in terms of both the asymptotic bias and coverage accuracy of the associated interval for out-of-sample evaluation, K-fold CV provably cannot outperform plug-in regardless of the rate at which the parametric or nonparametric models converge. Leave-one-out CV can have a smaller bias as compared to plug-in;however, this bias improvement is negligible compared to the variability of the evaluation, and in some important cases leave-one-out again does not outperform plug-in once this variability is taken into account. We obtain our theoretical comparisons via a novel higher-order Taylor analysis that allows us to derive necessary conditions for limit theorems of testing evaluations, which applies to model classes that are not amenable to previously known sufficient conditions. Our numerical results demonstrate that plug-in performs indeed no worse than CV across a wide range of examples. © 2024, CC BY.

关键词： Contrastive Learning

FINE-TUNING OF DIFFUSION MODELS VIA STOCHASTIC CONTROL: ENTROPY REGULARIZATION AND BEYOND

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arXiv 2024年

作者： Tang, Wenpin Department of Industrial Engineering and Operations Research Columbia University United States

This paper aims to develop and provide a rigorous treatment to the problem of entropy regularized fine-tuning in the context of continuous-time diffusion models, which was recently proposed by Uehara et al. (arXiv:2402.15194, 2024). The idea is to use stochastic control for sample generation, where the entropy regularizer is introduced to mitigate reward collapse. We also show how the analysis can be extended to fine-tuning involving a general f-divergence regularizer. Copyright © 2024, The Authors. All rights reserved.

关键词： Constrained optimization

CONVERGENCE OF COORDINATE ASCENT VARIATIONAL INFERENCE FOR LOG-CONCAVE MEASURES VIA OPTIMAL TRANSPORT

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arXiv 2024年

作者： Arnese, Manuel Lacker, Daniel Department of Industrial Engineering & Operations Research Columbia University United States

Mean field variational inference (VI) is the problem of finding the closest product (factorized) measure, in the sense of relative entropy, to a given high-dimensional probability measure ρ. The well known Coordinate Ascent Variational Inference (CAVI) algorithm aims to approximate this product measure by iteratively optimizing over one coordinate (factor) at a time, which can be done explicitly. Despite its popularity, the convergence of CAVI remains poorly understood. In this paper, we prove the convergence of CAVI for log-concave densities ρ. If additionally log ρ has Lipschitz gradient, we find a linear rate of convergence, and if also ρ is strongly log-concave, we find an exponential rate. Our analysis starts from the observation that mean field VI, while notoriously non-convex in the usual sense, is in fact displacement convex in the sense of optimal transport when ρ is log-concave. This allows us to adapt techniques from the optimization literature on coordinate descent algorithms in Euclidean space. Copyright © 2024, The Authors. All rights reserved.

关键词： Iterative methods

Is cross-validation the gold standard to estimate out-of-sample model performance? 24

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Is cross-validation the gold standard to estimate out-of-sam...

Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Garud Iyengar Henry Lam Tianyu Wang Department of Industrial Engineering and Operations Research Columbia University New York NY

ISBN: (纸本)9798331314385

Cross-Validation (CV) is the default choice for estimate the out-of-sample performance of machine learning models. Despite its wide usage, their statistical benefits have remained half-understood, especially in challenging nonparametric regimes. In this paper we fill in this gap and show that, in terms of estimating the out-of-sample performances, for a wide spectrum of models, CV does not statistically outperform the simple "plug-in" approach where one reuses training data for testing evaluation. Specifically, in terms of both the asymptotic bias and coverage accuracy of the associated interval for out-of-sample evaluation, K-fold CV provably cannot outperform plug-in regardless of the rate at which the parametric or nonparametric models converge. Leave-one-out CV can have a smaller bias as compared to plug-in; however, this bias improvement is negligible compared to the variability of the evaluation, and in some important cases leave-one-out again does not outperform plug-in once this variability is taken into account. We obtain our theoretical comparisons via a novel higher-order Taylor analysis that dissects the limit theorems of testing evaluations, which applies to model classes that are not amenable to previously known sufficient conditions. Our numerical results demonstrate that plug-in performs indeed no worse than CV in estimating model performance across a wide range of examples.

关键词：

CONTRACTIVE DIFFUSION PROBABILISTIC MODELS

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arXiv 2024年

作者： Tang, Wenpin Zhao, Hanyang Department of Industrial Engineering and Operations Research Columbia University United States

Diffusion probabilistic models (DPMs) have emerged as a promising technique in generative modeling. The success of DPMs relies on two ingredients: time reversal of diffusion processes and score matching. In view of possibly unguaranteed score matching, we propose a new criterion – the contraction property of backward sampling in the design of DPMs, leading to a novel class of contractive DPMs (CDPMs). Our key insight is that, the contraction property can provably narrow score matching errors and discretization errors, thus our proposed CDPMs are robust to both sources of error. For practical use, we show that CDPM can leverage weights of pretrained DPMs by a simple transformation, and does not need retraining. We corroborated our approach by experiments on synthetic 1-dim examples, Swiss Roll, MNIST, CIFAR-10 32×32 and AFHQ 64×64 dataset. Notably, CDPM steadily improves the performance of baseline score-based diffusion models. © 2024, CC BY.

关键词： Stochastic systems