On the Complexity of Trial and Error Shengyu Zhang Joint work with Xiaohui Bei and Ning Chen STOC'13,also at arXiv:1205.1183
Shengyu Zhang Joint work with Xiaohui Bei and Ning Chen STOC’13, also at arXiv:1205.1183
Motivating example:drug development Pandemic Consider an infectious disease outbreak due to an unknown virus. 。 Biochemists:find diagnosticreagents that have no serious side effects... ...as quickly as possible! PANDEMIC (Simplified)formulation Each side effect:certain combination of some ingredients Goal:find effective reagent/medicine without major side effect
Motivating example: drug development 2 • Consider an infectious disease outbreak due to an unknown virus. • Biochemists: find diagnostic reagents that have no serious side effects… … as quickly as possible! Pandemic • Each side effect: certain combination of some ingredients • Goal: find effective reagent/medicine without major side effect. (Simplified) formulation
Known vs.unknown If the virus(its DNA sequence,chemical composition,...) and its interactions to human body are known,then the reagent is much easier to find. Unfortunately,often the virus causing a pandemic is largely unidentified human body is too complicated a system to fully understand ●Learn it first?Efficiency！ 3
If the virus (its DNA sequence, chemical composition, …) and its interactions to human body are known, then the reagent is much easier to find. Unfortunately, often the virus causing a pandemic is largely unidentified. human body is too complicated a system to fully understand Learn it first? Efficiency! 3 Known vs. unknown
Standard method for drug development:Trial and error Candidate reagent allergic reaction, No side effect Side effect severe headache, MISSION ACCOMPLISHED 4
Candidate reagent No side effect Side effect 4 Standard method for drug development: Trial and error allergic reaction, severe headache, …
Phenomena Task:search for a solution (reagents)to satisfy a bunch of constraints(no side effect). Input(virus,human body):unknown. Allowed operations:solution testing. Approach:trial-and-error. Efficiency is crucial preferably better than learning the unknown input. ●Next:More examples. 5
Task: search for a solution (reagents) to satisfy a bunch of constraints (no side effect). Input (virus, human body): unknown. Allowed operations: solution testing. Approach: trial-and-error. Efficiency is crucial preferably better than learning the unknown input. Next: More examples. 5 Phenomena
Normal-Form Game Prisoner's Normal-form game dilemma Two (or more)players.Pi has a set Si of strategies. C D ·Joint strategy:s=(s1,S2)eS=S1×S2. C -1,-1 -10,0 ·Utility functions:ui:S→R. D 0,-10 -5,-5 Nash equilibrium A stable state where no player is willing to deviate her current strategy. Existence:(Mixed)Nash equilibrium alwaysexists.(vNM'44,N'51) Players have to Issue:In many scenarios,players do not know their payoffs. choose an action anyway Eg.:When a new business model appears,companies don't really know strategies will give how much payoff. 6
6 Normal-Form Game Issue: In many scenarios, players do not know their payoffs. • Eg.: When a new business model appears, companies don’t really know what strategies will give how much payoff. C D C -1, -1 -10, 0 D 0, -10 -5, -5 Prisoner’s dilemma • A stable state where no player is willing to deviate her current strategy. • Existence: (Mixed) Nash equilibrium always exists. (vNM’44, N’51) Nash equilibrium • Two (or more) players. 𝑃𝑖 has a set 𝑆𝑖 of strategies. • Joint strategy: 𝑠 = 𝑠1, 𝑠2 ∈ 𝑆 = 𝑆1 × 𝑆2. • Utility functions: 𝑢𝑖 : 𝑆 → ℝ. Normal-form game
Stable Matching Stable Matching Each individual has a preference over the agents of the other side Stable matching:no(m,w)preferring each other to their current ones 。 Gale-Shapley algorithm computes a stable matching Applications:hospital-intern allocation,school admission,... W1>W2>W3>W4 mi W1 m3>m1>m2>m4 W1>W2>W3>W4 1m2 W2 m3>m4>m1>m2 W2>W1>W3>W4 m3 W3 m1>m4>m2>m3 W3>W2>W4>W1 m4 W4 m4>m1>m3>m2 7
7 Stable Matching • Each individual has a preference over the agents of the other side • Stable matching: no (𝑚, 𝑤) preferring each other to their current ones • Gale-Shapley algorithm computes a stable matching • Applications: hospital-intern allocation, school admission, … Stable Matching 7 𝑚3 > 𝑚1 > 𝑚2 > 𝑚4 𝑚3 > 𝑚4 > 𝑚1 > 𝑚2 𝑚1 > 𝑚4 > 𝑚2 > 𝑚3 𝑚4 > 𝑚1 > 𝑚3 > 𝑚2 𝑤1 > 𝑤2 > 𝑤3 > 𝑤4 𝑚1 𝑤1 𝑤1 > 𝑤2 > 𝑤3 > 𝑤4 𝑤2 > 𝑤1 > 𝑤3 > 𝑤4 𝑤3 > 𝑤2 > 𝑤4 > 𝑤1 𝑚2 𝑚3 𝑚4 𝑤2 𝑤3 𝑤4
Stable Matching Stable Matching Issue:Individuals may not know their preferences exactly. Dating A man doesn't know how well a woman matches him as a wife until they are together for some time. Job market A candidate may not know precisely how much she likes the job. Also generally hard for recruiters to judge which candidates best fit the position. a systematic and continuous approach to fitting the right person to the An assignment right time has long been the Holy Grail of workforce organization." has to be ---McKinsey Quarterly,2003 determined 8
Stable Matching 8 Stable Matching Issue: Individuals may not know their preferences exactly. • A man doesn’t know how well a woman matches him as a wife until they are together for some time. Dating • A candidate may not know precisely how much she likes the job. • Also generally hard for recruiters to judge which candidates best fit the position. Job market “… a systematic and continuous approach to fitting the right person to the right job at the right time has long been the Holy Grail of workforce organization.” --- McKinsey Quarterly, 2003
In a broad sense Natural sciences Original Artist Reproduction rights.obtainable from www.CartoonStock.com- ·Hypothesis(theory) proposed.(Sometimes 2 predictions also made.) Experiment conducted to test it. If violation appears, reexamine the theory and propose new ones. 9
9 In a broad sense • Hypothesis (theory) proposed. (Sometimes predictions also made.) • Experiment conducted to test it. • If violation appears, reexamine the theory and propose new ones. Natural sciences
In a broad sense Natural Product design and sciences experiments ·Hypothesis(theory) Design and Analysis proposed.(Sometimes of Experiments predictions also made.) Experiment conducted to test it. If violation appears, reexamine the theory and ghih Edaio网 DOUGLAS C MONTGOMERY propose new ones. International Student Version 10
Product design and experiments 10 In a broad sense • Hypothesis (theory) proposed. (Sometimes predictions also made.) • Experiment conducted to test it. • If violation appears, reexamine the theory and propose new ones. Natural sciences