Evolutionary Bayesian Agents

A simulation of evolving populations of Bayesian agents learning to forage in environments with hidden causal structure.

Core Insight

Two timescales of adaptation:

Timescale	Mechanism	What Adapts
Ontogenetic (within lifetime)	Bayesian inference	Beliefs (probability distributions)
Phylogenetic (across generations)	Natural selection	Cognitive architecture (genome)

The genome specifies how to learn; learning fills in what is believed.

Quick Start

# Interactive mode — curses visualization of population foraging
uv run main.py

# Batch mode — text-only evolutionary run
uv run main.py --batch

# Options
uv run main.py --reality interaction --population 50 --generations 100
uv run main.py --batch --reality hierarchical

Controls (interactive mode)

• SPACE — pause / resume
• q — quit
• +/- — adjust simulation speed

What you'll see

• Grid: Food items rendered as coloured shapes (●, ■, ▲, ⬡) and agents as @
• Stats: Generation, tick, alive/total agents, mean/max fitness, survival rate
• Beliefs: The best agent's current learned beliefs about food types

Available Realities

Reality	Description	What Agents Should Learn
simple	Independent shape + color effects	Shape and color each matter
interaction	Shape-color combinations	Green circles are super-nutritious
hierarchical	Multi-level dependencies	Temperature affects texture safety
temporal	Time-varying effects	Hidden cycles, real-world time
hidden	Hidden variables	Position matters, but can't be seen

Architecture

┌─────────────────────────────────────────────────────────────────┐
│  REALITY (defined by the "god" — can be arbitrarily complex)    │
│  • True causal structure of food → energy                       │
│  • May include hidden variables agents cannot perceive          │
└─────────────────────────────────────────────────────────────────┘
                              │ observations (filtered by genome)
                              ▼
┌─────────────────────────────────────────────────────────────────┐
│  AGENT (genome specifies structure, learning fills parameters)  │
│  • Sensors: which attributes can be perceived                   │
│  • BN structure: which variables are modelled as relevant       │
│  • Priors: initial beliefs before learning                      │
└─────────────────────────────────────────────────────────────────┘
                              │ actions → outcomes
                              ▼
┌─────────────────────────────────────────────────────────────────┐
│  SELECTION                                                      │
│  • Fitness = net energy (gained − spent)                        │
│  • Fitter agents reproduce; their genomes propagate             │
└─────────────────────────────────────────────────────────────────┘

Project Structure

bayesian-agent/
├── main.py              # Entry point: interactive (curses) or batch mode
├── reality.py           # Ground truth causal structure of the world
├── cognitive_genome.py  # Heritable cognitive architecture specification
├── bayesian_agent.py    # Agents that learn via Bayesian inference + populations
├── simulation.py        # Evolutionary simulation driver
├── visualization.py     # Curses-based population renderer
└── pyproject.toml       # Dependencies (just numpy)

Key Concepts

The Genome

Encodes:

1. Sensors — which attributes the agent can perceive (e.g., SHAPE, COLOR, TEMPERATURE)
2. BN Structure — which perceived attributes are modelled as relevant to energy
3. Priors — initial belief parameters (mean, variance, pseudo-observations)

The genome does NOT encode actual beliefs — those are learned within a lifetime.

Bayesian Learning

Agents update beliefs using conjugate Normal-Normal inference:

P(μ | observations) ~ Normal(posterior_mean, posterior_variance)

Each configuration of relevant variables gets its own belief distribution.

Thompson Sampling

Agents use Thompson sampling for exploration-exploitation: sample from the posterior, pick the food with highest sampled value minus travel cost.

Evolution

Across generations:

1. Agents with higher fitness reproduce
2. Offspring inherit mutated cognitive architectures
3. Architectures that enable better learning propagate

References

• Friston (2010). The free-energy principle: a unified brain theory?
• Baldwin (1896). A New Factor in Evolution
• Hinton & Nowlan (1987). How Learning Can Guide Evolution
• Russo et al. (2018). A Tutorial on Thompson Sampling

License

MIT