Computational evolution of

decision-making strategies

Peter KvamCenter for Adaptive Rationality, Max Planck Institute for Human Development

Department of Psychology, Michigan State University

Joseph CesarioDepartment of Psychology, Michigan State University

Jory SchossauDepartment of Computer Science and Engineering, Michigan State University

Heather EisthenDepartment of Integrative Biology, Michigan State University

Arend HintzeDepartment of Integrative Biology, Michigan State University

Introduction

• We often take a strategy-first approach when

constructing decision-making models

– Assume optimal, approximately optimal, specific heuristics,

utility-based, or other principled strategy

– Then see what practical limitations are and in what environments

it succeeds

– Success = strategy is adaptive

• This is a bit backwards

– In reality, strategies are adaptive because they arise from the

environment, not vice versa

– We instead take the opposite approach, examining strategies

that evolve in response to task environment

Introduction

• Computational evolution approach

– Evolve artificial agents using mechanisms

that are similar to natural selection

– Guarantees adaptive strategies

– Biologically based agents easy to

implement on neural hardware

• Allows us to evolve decision-making

strategies and compare against

existing theories

– More complex / more information used

• Optimal sampling models (e.g. high-

threshold diffusion)

– Less complex / less information used

• Heuristic strategies (e.g. run rules)

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Goals

• Examine a common task that animals in almost every ecological niche have to solve– Binary perceptual decision

• Incoming information is from source A or source B -- agent must determine which one

• e.g. predator / prey, edible / inedible, track A / B

– Optional stopping (agent terminates search)

• Examine strategies that they develop– Examine structure of their brains

– Behavioral accuracy, brain complexity, amount of information use

Methods

• Task

– Discriminate between sources of incoming information

– Comes from either majority [01] (right) or majority [10] (left)

• Agents

– Markov brains (16-bit)

• Have 16 nodes, used for input, processing, output of information

• Nodes are causally connected via logic gates

• Genetic code gives rise to pattern of connections

Markov Brain

Markov Brain

Inputs come from:

A) N% 1s on left, N% 0s on right

B) N% 0s on left, N% 1s on right

Difficulty manipulated by changing N

(high [e.g. 90] = easy, low [e.g. 60] = difficult)

Markov Brain

N = 90%, LEFT on this trial

Difficulty manipulated by changing N

(high [e.g. 90] = easy, low [e.g. 60] = difficult)

81%

9%

9%

1%

Markov Brain

Organism has to indicate which one using its output nodes

Markov Brain

Markov Brain

Markov Brain

Markov Brain

Markov Brain

Markov Brain

Setup

• 100 organisms per generation

– Each one has its own genome and node structure

• Each organism makes 100 left [10] / right [01] decisions

during its lifetime (actual direction is random)

– Gains points for every correct answer, loses points for incorrect

• Reproduction based on performance (roulette wheel)

– Offspring accumulate mutations in genome to set node structure

– Poor performers simply die off without reproducing

Data

• Focus on manipulations of difficulty

• Fitness – asymptotic performance of population

• Brain size - # of connections between nodes in the

artificial brains

• Strategy use – how much information do the agents

use, and how long do they gather it?

Fitness

90% 85% 80% 75%

70% 65% 60%

• Agents achieved near-

perfect accuracy in

most conditions except

most difficult

• Even then, worst

performance was

~80% accuracy

Strategies

• Simple heuristic strategies

– Should use very little information

– Terminate search early

– Small brains

• Complex evidence accumulation strategies

– Should use a large amount of information

– Gather information over a protracted period

– Large brains

Results – brain size

• Brain size

– Generally larger in more difficult conditions

– Response to more demanding task environment

• Brains decreased in size when the task was easy

– Despite no explicit cost for more connections

– Seems to result from the mutation load imposed by larger brain

Results – strategy use

• More difficult conditions led to more information use– Agents also gathered information over a more protracted period

Conclusions

• Difficulty of task environment plays a huge role in evolutionary trajectory of artificial agents– Behavior scales based on environmental demands,

– Not strictly based on optimal decision strategies

• Agents in difficult conditions evolved large brains, integrated lots of information over a protracted period– Strategies resembled complex sequential sampling strategies

• Agents in easier conditions evolved smaller brains, used relatively little information– Brain size seems to be limited by mutation load

– Strategies resembled 2-run / 3-run heuristic rules

Bonus slides

• Surface plots– Brain size

– Memory (self loops)

– Memory (back-and-forth loops)

– Mean decision time

• Cost-benefit payoff manipulations

• 1000 tick results– % correct

– Fitness

– Decision time

Brain size

Memory – self loops

Memory – back-and-forth loops

Waiting times

Cost-Benefit manipulations

1,000-tick Results - # Correct

1,000-tick Results - Fitness

1,000-tick Results – Decision time