NASA Workshop on Collectives Ames Lab, 6 August 2002 Complex System Management: Hoping for the Best by Coping with the Worst Hoping for the best. . . but coping with the worst Neil F. Johnson n. johnson@physics. ox. ac. uk Department of Physics, Oxford University, U. K. Collaborators on several of the projects discussed: P. Jefferies, D. Lamper, M. Hart, R. Kay, P. M. Hui & Damien Challet
Outline • • • Collectives & complex systems: design issues global outcomes: best-case vs. OK-case vs. worst-case static vs. dynamical § § Dynamical collectives: multi-agent models generalized binary games with time-dependent global resources deterministic vs. stochastic formalism undesirable outcomes -- system crashes & their control -- fate, or just bad luck ? immunization of a complex system/collective § § § Static collectives: optimal collectives of autonomous defects near-perfect combinations of defective components defective component + defective component = working device § § Winning by losing: optimal collectives of autonomous games successful combinations of unsuccessful games lose + lose = win, failure + failure = success, unsafe + unsafe = safe § § Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems
Topic • • • Collectives & complex systems: design issues global outcomes: best-case vs. OK-case vs. worst-case static vs. dynamical § § Dynamical collectives: multi-agent models generalized binary games with time-dependent global resources deterministic vs. stochastic formalism undesirable outcomes -- system crashes & their control -- fate, or just bad luck ? immunization of a complex system/collective § § § Static collectives: optimal collectives of autonomous defects near-perfect combinations of defective components defective component + defective component = working device § § Winning by losing: optimal collectives of autonomous games successful combinations of unsuccessful games lose + lose = win, failure + failure = success, unsafe + unsafe = safe § § Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems
• Complex Systems • Many degrees of freedom with internal frustration, feedback, history-dependence, adaptation, evolution, non-stationarity, non -equilibrium, memory, single realization, exogenous effects • Collectives, multi-agent systems, forward and inverse problems • Mix of deterministic and stochastic behavior • The Right Stuff System’s evolution can be optimized, controlled, managed. Robust • The Wrong Stuff System has a bad day. . . Heads down wrong path, leading to dangerous values, fluctuations, crashes. Endogenous and exogenous factors. Instabilities. Spontaneous secondary mission. Brittle • The Good Stuff System behaves OK, not great but not bad Avoids bad scenarios, e. g. system crash PLAN B may be ‘best’ e. g. lowest risk
§ § • • § Consider the global performance S(t) of a collective/complex system Examples [Workshop website, Tumer & Wolpert]: § throughput in a data network § total scientific information gathered by a constellation of deployable instruments § GDP growth in a human economy § percentage of available free energy exploited by an ecosystem The Right Stuff: optimize/maximize global performance S(t) mission successful The Good Stuff: § S(t) less/more than Scritical for all time t, or time-window T § <S(t)> less/more than Scritical for all time t, or time-window T § Var[ S(t) ] less/more than critical for all time t, or time-window T § < [ S(t) ]n > less/more than X for any n etc…. mission reasonably successful … not a disaster – mission not a disaster !
real-world static system’s time evolution S (t) ideal response L(t) = L actual response L + time …+1 …+2 …+3 …+4 …+5 e. g. minimize error by adjusting initial ‘quenched disorder’
real-world dynamical system’s time evolution S (t) global resource level L(t) …+1 …+2 deterministic vs. stochastic continuous vs. discrete known vs. unknown …+5 …+4 …+3 endogenous vs. exogenous
killer app: ‘designer system’ I system’s time evolution S (t) L(t) = L …+1 …+2 …+3 …+4 …+5 e. g. minimize ‘noise’, typical fluctuation size, hence optimize winnings, efficiency, use of global resource
killer app: ‘designer system’ II system’s time evolution S (t) time …+1 …+2 …+3 …+4 …+5 e. g. avoid ‘dangerous’ large changes
Complex Systems: Tails of the Unexpected Distribution of increments of S (t ) Typically Levy-like Sits somewhere between Lorentzian and Gaussian, but hard to tell since • finite dataset • non-stationarity Fat tails etc. are ‘obvious’ from statistics but … temporal correlations (e. g. system crashes) do not show up! big problem for standard risk analysis
Topic • • • Collectives & complex systems: design issues global outcomes: best-case vs. OK-case vs. worst-case static vs. dynamical § § Dynamical collectives: multi-agent models generalized binary games with time-dependent global resources deterministic vs. stochastic formalism undesirable outcomes -- system crashes & their control -- fate, or just bad luck ? immunization of a complex system/collective § § § Static collectives: optimal collectives of autonomous defects near-perfect combinations of defective components defective component + defective component = working device § § Winning by losing: optimal collectives of autonomous games successful combinations of unsuccessful games lose + lose = win, failure + failure = success, unsafe + unsafe = safe § § Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems
In general, define w(t) according to the game of interest don’t enter the game limited global at time t Challet & Zhang Binary game histories resource level SO. . WHAT’S THE GAME ? 0 S e. g. sell 1 e. g. buy N history at time t strategies . . 10 agent memory m = 2 history at time t +1 . . 01
Binary version of El Farol Game with time-dependent resource level (i. e. seating capacity) L(t) correlation between L(t) and A(t) system ‘learns’ frequency w system ‘confused’ attendance A (t) L(t)=L+L 0 sin w t time t
Deterministic map of binary game evolution § Binary games behave as a stochastically perturbed deterministic system Global information m (t) for m=2 Stochastic perturbations from coin-tossing agents Periods of entirely deterministic behaviour § Replace stochastic term from coin-tossing agents by its mean z Jefferies, Hart & NFJ Phys. Rev. E 65, 016105 (2002)
Deterministic map of binary game evolution § ‘ attendance ’ = ‘ demand ’ A ( t ) = n 1 (t) - n 0 (t) = D ( t ) [not always true!] ‘ volume ’ V ( t ) = n 1 (t) + n 0 (t) § S (t) strategy score vector [ PRE 65, 016105 (2002) ] § r confidence level § m (t) global information m {0, 1, . . P-1} P = 2 m § a m ( t ) response of strategies to m ( t ) ; a. R {-1, 1} strategy R § Y symmetrized strategy allocation tensor 3 0 4 0 0 5 2 0 0 3 0 0 0 7 0 1 0 7 0 0 4 7 0 6 0 1 0 0 4 0 0 s=2 Deterministic game defined by mapping equations: § Binary El Farol Game: w(t) = L(t) V(t) - n 1 (t) § MG: L(t)=0. 5 w(t) > 0 1 wins w (t) < 0 0 wins strategy R’ § 0 0 0 8 0 3 2 0 0 1 5 0 0 0 4 0 4 0 7 0 6 0 3 0 0 0 1 0 7 0 0 1 0 3 0 0 2 0 3 0 2 7 0 4 0 7 0 4 3 0 0 random matrix initial strategy allocation quenched disorder In general, success & payoff may not be so simple to define w(t) complicated functional form
Crowd - Anticrowd effect e. g. MG J. Phys. A: Math. Gen. 32, L 427 (1999) Physica A 298, 537 (2001) large crowds >> 0 wastage but 0 for • stochastic strategy use • mixed-ability populations coin-toss crowd - anticrowd pairs execute uncorrelated random walks sum of variances … also works for generalized games walk step-size # of walks
GCMG m =3 GCMG m =10 Jefferies & NFJ cond-mat/0207523 Design of generalized binary games $G 11 $G 13 m =3 $G 11 $G 13 m =10 dynamical properties very sensitive to game’s microstructure
Jefferies & NFJ, cond-mat/0201540 Lamper & NFJ, PRL 017902 (2002)
Jefferies & NFJ, cond-mat/0201540 Lamper & NFJ, PRL 017902 (2002) Anatomy of a system crash § During persistence demand described by: time during crash Assume: crash length: participating ‘crash’ nodes § Expected demand (and volume) during crash are thus given by:
Hart & NFJ cond-mat/0207588 Physica A (2002) in press system’s evolution Convergence of ‘parallel-world’ trajectories prior to crash : spread of paths indicates role of ‘fate’ vs. ‘bad luck’
Hart & NFJ cond-mat/0207588 Physica A (2002) in press Immunizing against system crash Protecting the system Can reduce chances of system crash, by forcing earlier down-movements system gets immunized
Topic • • • Collectives & complex systems: design issues global outcomes: best-case vs. OK-case vs. worst-case static vs. dynamical § § Dynamical collectives: multi-agent models generalized binary games with time-dependent global resources deterministic vs. stochastic formalism undesirable outcomes -- system crashes & their control -- fate, or just bad luck ? immunization of a complex system/collective § § § Static collectives: optimal collectives of autonomous defects near-perfect combinations of defective components defective component + defective component = working device § § Winning by losing: optimal collectives of autonomous games successful combinations of unsuccessful games lose + lose = win, failure + failure = success, unsafe + unsafe = safe § § Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems
Optimal collectives of autonomous defects e. g. nanodevice output, robot action, . . . Challet & NFJ, PRL 89, 028701 (2002) Tumer and Wolpert (2002) output ideal output L(t) = L actual output L + time …+1 …+2 …+3 …+4 …+5 N defective devices with a distribution of errors Combine a subset M < N to form high performance (i. e. low-error) collective: unconstrained, analog unconstrained, binary constrained, analog constrained, binary
Optimal collectives of autonomous defects e. g. nanodevice output, robot action, . . . error over average Challet & NFJ, PRL 89, 028701 (2002) all components Tumer and Wolpert (2002) med < > N = 10 N = 20 < > unconstrained, analog N devices random cost approach constrained, analog N devices
Optimal collectives of autonomous defects e. g. nanodevice output, robot action, . . . [Challet & NFJ, PRL (2002)] < > MG with agents accounting for their impact unconstrained, analog N devices 2 strategies per agent
Optimal collectives of autonomous defects e. g. nanodevice output, robot action, . . . [Challet & NFJ, PRL (2002)] N binary components 0. 2 simple enumeration 0. 25 0. 3 & sorting f Each component has I input bits Can perform F different logical operations, hence P = F 2 I transformations f = probability that component i systematically gives wrong output = fraction of component sets with at least one perfect subset unconstrained, binary N devices
Optimal collectives of autonomous defects e. g. component sets Optimum: average = fraction ofnanodevice output, robot action, . . . [Challet & over 10, 000 samples with at least one perfect subset. NFJ, PRL (2002)] 0. 2 simple enumeration 0. 25 0. 3 & sorting f unconstrained, binary N devices Majority Game: average over 300 samples, 500 P iterations 2 components/agent Majority Game constrains the system to M=N/2 Possible improvement with Grand Canonical Majority Game GCMaj. G ?
Topic • • • Collectives & complex systems: design issues global outcomes: best-case vs. OK-case vs. worst-case static vs. dynamical § § Dynamical collectives: multi-agent models generalized binary games with time-dependent global resources deterministic vs. stochastic formalism undesirable outcomes -- system crashes & their control -- fate, or just bad luck ? immunization of a complex system/collective § § § Static collectives: optimal collectives of autonomous defects near-perfect combinations of defective components defective component + defective component = working device § § Winning by losing: optimal collectives of autonomous games successful combinations of unsuccessful games lose + lose = win, failure + failure = success, unsafe + unsafe = safe § § Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems
Winning by losing game + losing game = winning game unsafe + unsafe = safe win GAME A rotate randomly by lose GAME B rotate randomly by Randomly playing Games A and B
Nash Switching randomly between 2 ‘losing’ games gives ‘winning’ game Pareto
J. Parrondo et al. PRL (1999) Generalization to 2 history-dependent games: R. Kay & NFJ cond-mat/0207386 Application to quantum computing: C. F. Lee & NFJ quant-ph/0203043 -1 +1 -1 -1 +1 +1 +1 -1
Topic • • • Collectives & complex systems: design issues global outcomes: best-case vs. OK-case vs. worst-case static vs. dynamical § § Dynamical collectives: multi-agent models generalized binary games with time-dependent global resources deterministic vs. stochastic formalism undesirable outcomes -- system crashes & their control -- fate, or just bad luck ? immunization of a complex system/collective § § § Static collectives: optimal collectives of autonomous defects near-perfect combinations of defective components defective component + defective component = working device § § Winning by losing: optimal collectives of autonomous games successful combinations of unsuccessful games lose + lose = win, failure + failure = success, unsafe + unsafe = safe § § Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems
Network games Eguiluz & Zimmerman, PRL 85, 5659 (2001) power-law tails Zheng, NFJ et al. , Eur. Phys. J. B 27, 213 (2002) Analytics using generating function tune power-law exponent Herding like-minded agents form clusters power-law distribution of cluster sizes & signal S(t)
Topic • • • Collectives & complex systems: design issues global outcomes: best-case vs. OK-case vs. worst-case static vs. dynamical § § Dynamical collectives: multi-agent models generalized binary games with time-dependent global resources deterministic vs. stochastic formalism undesirable outcomes -- system crashes & their control -- fate, or just bad luck ? immunization of a complex system/collective § § § Static collectives: optimal collectives of autonomous defects near-perfect combinations of defective components defective component + defective component = working device § § Winning by losing: optimal collectives of autonomous games successful combinations of unsuccessful games lose + lose = win, failure + failure = success, unsafe + unsafe = safe § § Topology of collectives: network-based multi-agent games Risk management in collectives & complex systems
![Risk management in collectives § borrow terminology from finance [c. f. Hogg, Huberman] §](https://present5.com/presentation/e978ac2a30931e00c51fba4af10c6c98/image-35.jpg "Risk management in collectives § borrow terminology from finance [c. f. Hogg, Huberman] §")
Risk management in collectives § borrow terminology from finance [c. f. Hogg, Huberman] § avoid standard local-in-time stochastic p. d. e. approach § allow for non-Gaussian, non-stationary distributions, temporal correlations § include friction due to communication/intervention costs § variation of global `wealth’: § apply ‘no free lunch’ § minimize the ‘risk’ by choosing a suitable risk-management strategy
no risk management probability mission unsuccessful change in ‘wealth’ of system mission successful
risk management … but assume no friction i. e. it ‘costs’ nothing to intervene 3 interventions probability 30 interventions change in ‘wealth’ of system standard deviation of ‘wealth’ distribution time between interventions
risk management … and friction i. e. it ‘costs’ something to intervene 3 interventions probability 30 interventions change in ‘wealth’ of system standard deviation of ‘wealth’ distribution there is an ‘optimal’ time-delay between interventions time between interventions
Скачать презентацию NASA Workshop on Collectives Ames Lab 6 August
e978ac2a30931e00c51fba4af10c6c98.ppt