Learning, Markets, and Exponential Families Financialization of ML - PowerPoint PPT Presentation

Learning, Markets, and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Learning, Markets, and Exponential Families Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ Jacob Abernethy Markets University of Michigan Department of Computer Science and Engineering November 14, 2014

Learning, Markets, A Bird-Eye view of Learning Theory and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Financialization of ML Outline We want to design algorithms that take data as input and Market Making ≈ return predictions as output. But there are fundamental OLO limits to our ability to predict and how quickly we can Exp. Families ≈ Markets achieve good performance. Two driving questions ◮ How well can we learn given very limited data? ◮ What are the computational challenges of prediction?

Learning, Markets, An Economic Translation and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Financialization of ML Thinking in terms of the economic tradeoffs , our goal is to Outline Market Making ≈ determine the equilibrium point among the following: OLO ◮ The marginal cost of additional data Exp. Families ≈ Markets

Learning, Markets, An Economic Translation and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Financialization of ML Thinking in terms of the economic tradeoffs , our goal is to Outline Market Making ≈ determine the equilibrium point among the following: OLO ◮ The marginal cost of additional data Exp. Families ≈ Markets ◮ The marginal value of performance improvement (i.e. better decision making)

Learning, Markets, An Economic Translation and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Financialization of ML Thinking in terms of the economic tradeoffs , our goal is to Outline Market Making ≈ determine the equilibrium point among the following: OLO ◮ The marginal cost of additional data Exp. Families ≈ Markets ◮ The marginal value of performance improvement (i.e. better decision making) ◮ The marginal cost of computational resources

Learning, Markets, An Economic Translation and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Financialization of ML Thinking in terms of the economic tradeoffs , our goal is to Outline Market Making ≈ determine the equilibrium point among the following: OLO ◮ The marginal cost of additional data Exp. Families ≈ Markets ◮ The marginal value of performance improvement (i.e. better decision making) ◮ The marginal cost of computational resources ◮ The marginal value of time

Learning, Markets, Financialization of ML and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ In 6 Slides Markets

Learning, Markets, 1. Data Brokerage and Exponential Families Jacob Abernethy In the world of Big Data, buying and selling information is a Intro: Economics growing industry. Learning Learning ≈ Tradeoffs Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ Markets

Learning, Markets, 2. Algorithms as a Service and Exponential Families Jacob Abernethy Intro: Economics Learning All-purpose ML algorithms are being provided as a web Learning ≈ Tradeoffs service and sold to developers. Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ Markets

Learning, Markets, 3. Information Markets and Exponential Families Markets built entirely for speculative purposes, where traders Jacob Abernethy can buy/sell securities on elections results to football Intro: Economics Learning matches, have flourished in recent years. Learning ≈ Tradeoffs Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ Markets

Learning, Markets, 4. A Market for Cycles and Exponential Families Jacob Abernethy There is an emerging competitive market where unit of Intro: Economics Learning computation are sold like a commodity Learning ≈ Tradeoffs Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ Markets

Learning, Markets, 5. A Market for Solutions and Exponential Families Companies are starting to turn towards the prize-driven Jacob Abernethy competition to solve big data challenges, rather than hiring Intro: Economics in-house data scientists. Learning Learning ≈ Tradeoffs Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ Markets

Learning, Markets, 6. Market for Academics and Exponential Families Jacob Abernethy ML Practitioners (including many academics and graduate Intro: Economics students) have apparently risen in value in recent years. Learning Learning ≈ Tradeoffs Financialization of ML Outline Market Making ≈ OLO Exp. Families ≈ Markets

Learning, Markets, This Talk and Exponential Families Jacob Abernethy Intro: Economics Learning Learning ≈ Tradeoffs Financialization of ML We will discuss some recent results connecting Outline learning-theoretic ideas to finance and economic questions. Market Making ≈ OLO ◮ Intro Exp. Families ≈ Markets ◮ Quick review of regret minimization ◮ Regret in the context of market making ◮ Exponential family distributions viewed as a prediction market mechanism

Learning, Markets, The Typical Regret-minimization Framework and Exponential Families Jacob Abernethy We imagine an online game between Nature and Learner. Intro: Economics Learner has a (typically convex) decision set X ⊂ R d , and Learning Learning ≈ Tradeoffs Nature has an action set Z , and there is a loss function Financialization of ML Outline ℓ : X × Z → R defined in advance. Market Making ≈ OLO Exp. Families ≈ Markets

Learning, Markets, The Typical Regret-minimization Framework and Exponential Families Jacob Abernethy We imagine an online game between Nature and Learner. Intro: Economics Learner has a (typically convex) decision set X ⊂ R d , and Learning Learning ≈ Tradeoffs Nature has an action set Z , and there is a loss function Financialization of ML Outline ℓ : X × Z → R defined in advance. Market Making ≈ OLO Online Convex Optimization Exp. Families ≈ For t = 1 , . . . , T : Markets ◮ Learner chooses x t ∈ X ◮ Nature chooses z t ∈ Z ◮ Learner suffers ℓ ( x t , z t ) Learner is concerned with the regret : � T � T t =1 ℓ ( x t , z t ) − min x ∈X t =1 ℓ ( x , z t )

Learning, Markets, The Typical Regret-minimization Framework and Exponential Families Jacob Abernethy We imagine an online game between Nature and Learner. Intro: Economics Learner has a (typically convex) decision set X ⊂ R d , and Learning Learning ≈ Tradeoffs Nature has an action set Z , and there is a loss function Financialization of ML Outline ℓ : X × Z → R defined in advance. Market Making ≈ OLO Online Convex Optimization Exp. Families ≈ For t = 1 , . . . , T : Markets ◮ Learner chooses x t ∈ X ◮ Nature chooses z t ∈ Z ◮ Learner suffers ℓ ( x t , z t ) Learner is concerned with the regret : � T � T t =1 ℓ ( x t , z t ) − min x ∈X t =1 ℓ ( x , z t ) This talk we assume ℓ is linear in x ; WLOG ℓ ( x t , z t ) = x ⊤ z t .

Learning, Markets, Follow the Regularized Leader and Exponential Families Jacob Abernethy FTRL – Primal Version Intro: Economics Learning 1: Input: learning rate η > 0, regularizer R : X → R Learning ≈ Tradeoffs Financialization of ML t − 1 Outline � x ⊤ l s . 2: for t = 1 . . . T , x t ← − arg min x ∈X R ( x ) + η Market Making ≈ OLO s =1 Exp. Families ≈ Markets

Learning, Markets, Follow the Regularized Leader and Exponential Families Jacob Abernethy FTRL – Primal Version Intro: Economics Learning 1: Input: learning rate η > 0, regularizer R : X → R Learning ≈ Tradeoffs Financialization of ML t − 1 Outline � x ⊤ l s . 2: for t = 1 . . . T , x t ← − arg min x ∈X R ( x ) + η Market Making ≈ OLO s =1 Exp. Families ≈ Markets FTRL – Dual Version � t − 1 � � − ∇ R ∗ 1: for t = 1 . . . T , x t ← − η l s . s =1

Learning, Markets, Follow the Regularized Leader and Exponential Families Jacob Abernethy FTRL – Primal Version Intro: Economics Learning 1: Input: learning rate η > 0, regularizer R : X → R Learning ≈ Tradeoffs Financialization of ML t − 1 Outline � x ⊤ l s . 2: for t = 1 . . . T , x t ← − arg min x ∈X R ( x ) + η Market Making ≈ OLO s =1 Exp. Families ≈ Markets FTRL – Dual Version � t − 1 � � − ∇ R ∗ 1: for t = 1 . . . T , x t ← − η l s . s =1 FTRL is essentially the “only” algorithm we have. (This COLT: even Follow the Perturbed Leader is a special case of FTRL [Abernethy, Lee, Sinha, and Tewari, 2014b]