Robust Experimentation in the Continuous Time Bandit Problem

Pourbabaee, Farzad

doi:10.2139/ssrn.3189845

Cited by 3 publications

(5 citation statements)

References 31 publications

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“…General nonconvexconcave problems can be solved by a simple gradient descent-ascent (GDA) scheme combined with quadratic regularization in y, with iteration complexity O(ε −5 ) [53]. 6 More elaborate algorithmic schemes based on the proximal-point method have O(ε −3 ) iteration complexity [54,95,55,57]. Here we propose a GDA-type scheme in the form of Algorithm 2.…”

Section: Algorithms Based On the Constant And Linear Approximationsmentioning

confidence: 99%

“…This allows to regularize with ρ = ρ 1 and results in ε-independent smoothness O( λ1 + µ 2 ρ 1 ) of the corresponding primal function. 6 This estimate follows from the complexity…”

Section: Algorithms Based On the Constant And Linear Approximationsmentioning

confidence: 99%

“…In the past few years, min-max optimization has become popular among practitioners due to its relevance for machine learning applications-in particular, when training generative adversarial networks (GANs) [1,2,3,4], robust machine learning [5,6,7,8,9,10], in fair statistical inference [11,12,13,14,15,16], in reinforcement learning [17], distributed optimization and learning over networks [18,19,20,21,22], and for optimal resource allocation in multi-agent systems [23,24]. The common task arising in these applications, as well as in many others, is solving optimization problems of the general form min…”

Section: Introductionmentioning

confidence: 99%

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Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain

Ostrovskii,

Barazandeh,

Razaviyayn

2021

Preprint

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We study the problem of finding approximate first-order stationary points in optimization problems of the form min x∈X max y∈Y f (x, y), where the sets X, Y are convex and Y is compact. The objective function f is smooth, but assumed neither convex in x nor concave in y. Our approach relies upon replacing the function f (x, ⋅) with its k-th order Taylor approximation (in y) and finding a near-stationary point in the resulting surrogate problem. To guarantee its success, we establish the following result: let the Euclidean diameter of Y be small in terms of the target accuracy ε, namely O(ε 2 k+1 ) for k ∈ N and O(ε) for k = 0, with the constant factors controlled by certain regularity parameters of f ; then any ε-stationary point in the surrogate problem remains O(ε)-stationary for the initial problem. Moreover, we show that these upper bounds are nearly optimal: the aforementioned reduction provably fails when the diameter of Y is larger. For 0 ⩽ k ⩽ 2 the surrogate function can be efficiently maximized in y; our general approximation result then leads to efficient algorithms for finding a near-stationary point in nonconvex-nonconcave min-max problems, for which we also provide convergence guarantees.

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Section: Algorithms Based On the Constant And Linear Approximationsmentioning

confidence: 99%

“…This allows to regularize with ρ = ρ 1 and results in ε-independent smoothness O( λ1 + µ 2 ρ 1 ) of the corresponding primal function. 6 This estimate follows from the complexity…”

Section: Algorithms Based On the Constant And Linear Approximationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain

Ostrovskii,

Barazandeh,

Razaviyayn

2021

Preprint

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“…Now suppose the contract (s GP (I), s GP (R)) is offered to the GP. Similar to the binary case, the contract should satisfy s GP (I) ≥ p i s GP (R) (17) to make sure that GP does not invest in the bad project. Once offered, the agent chooses effort λ i which is the solution to the problem max…”

Section: And Cmentioning

confidence: 99%

Optimal Design of Limited Partnership Agreements

Rezaei¹

2021

Preprint

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General partners (GP) are sometimes paid on a deal-by-deal basis and other times on a whole-portfolio basis. When is one method of payment better than the other? I show that when assets (projects or firms) are highly correlated or when GPs have low reputation, whole-portfolio contracting is superior to deal-by-deal contracting. In this case, by bundling payouts together, whole-portfolio contracting enhances incentives for GPs to exert effort. Therefore, it is better suited to alleviate the moral hazard problem which is stronger than the adverse selection problem in the case of high correlation of assets or low reputation of GPs. In contrast, for low correlation of assets or high reputation of GPs, information asymmetry concerns dominate and deal-bydeal contracts become optimal, as they can efficiently weed out bad projects one by one. These results shed light on recent empirical findings on the relationship between investors and venture capitalists.

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“…( 1) minimizes the worse data distribution. Prior studies [2,3,4,15,42] considered different uncertainty sets (see Definition 3.1 in [15]) for which they proposed equivalent reformulations of Eq. (1) based on the specific choice of U m .…”

Section: Introductionmentioning

confidence: 99%

Learning Distributionally Robust Models at Scale via Composite Optimization

Haddadpour¹,

Kamani²,

Mahdavi³

et al. 2022

Preprint

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To train machine learning models that are robust to distribution shifts in the data, distributionally robust optimization (DRO) has been proven very effective. However, the existing approaches to learning a distributionally robust model either require solving complex optimization problems such as semidefinite programming or a first-order method whose convergence scales linearly with the number of data sampleswhich hinders their scalability to large datasets. In this paper, we show how different variants of DRO are simply instances of a finite-sum composite optimization for which we provide scalable methods. We also provide empirical results that demonstrate the effectiveness of our proposed algorithm with respect to the prior art in order to learn robust models from very large datasets.

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Robust Experimentation in the Continuous Time Bandit Problem

Cited by 3 publications

References 31 publications

Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain

Nonconvex-Nonconcave Min-Max Optimization with a Small Maximization Domain

Optimal Design of Limited Partnership Agreements

Learning Distributionally Robust Models at Scale via Composite Optimization

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