Bayesian decision-theoretic agents — expected utility maximisation, not prompt engineering
Project description
Credence
Bayesian decision-theoretic agents — a reusable library and an empirical benchmark.
Credence provides domain-agnostic Bayesian agents that learn tool reliability from experience, use value-of-information calculations to decide when to query and when to abstain, and adapt when reliability changes. No heuristics, no hardcoded routing — just expected utility maximisation.
The project also includes a head-to-head benchmark comparing the Bayesian agent against LangChain ReAct agents on a multi-tool question-answering task.
Using Credence as a Library
# Core library (numpy + scipy only)
uv sync
# With benchmark dependencies (matplotlib, langchain, etc.)
uv sync --extra benchmark
# With dev tools (pytest, ruff, etc.)
uv sync --extra dev
Facade import
from credence import BayesianAgent, ToolConfig, ScoringRule
Minimal custom-domain example
import numpy as np
from credence import BayesianAgent, ToolConfig, ScoringRule
# Define your domain's categories and tools
categories = ("plot", "character", "setting", "theme")
num_cats = len(categories)
tools = [
ToolConfig(cost=1.0, coverage_by_category=np.ones(num_cats)), # wiki_search
ToolConfig(cost=3.0, coverage_by_category=np.ones(num_cats)), # deep_read
ToolConfig(cost=2.0, coverage_by_category=np.ones(num_cats)), # summary_llm
]
# Category inference: question text -> probability vector over categories
# (or use make_keyword_category_infer_fn for keyword-based heuristics)
def infer_category(text: str) -> np.ndarray:
return np.ones(num_cats) / num_cats # uniform prior
agent = BayesianAgent(
tool_configs=tools,
categories=categories,
category_infer_fn=infer_category,
)
Categories, tools, scoring rules, and the category inference function are all injected — the agent itself is domain-agnostic.
The Benchmark
A head-to-head comparison between a Bayesian decision-theoretic agent and LangChain ReAct agents on a multi-tool question-answering task.
Both agents have access to the same four tools with heterogeneous, category-dependent reliability. The Bayesian agent learns tool reliability from experience and uses value-of-information calculations to decide when to query, when to cross-verify, and when to abstain. The LangChain agent lets the LLM decide.
Running experiments
# Run tests
uv run pytest -v
# Run all experiments (stationary + drift + ablation)
uv run python -m experiments.run_full_comparison
# Or run individually
uv run python -m experiments.run_stationary --seeds 20
uv run python -m experiments.run_drift --seeds 20
uv run python -m experiments.run_ablation --seeds 20
LangChain agents require a local Ollama instance with llama3.1 (default).
Set CREDENCE_LLM_PROVIDER=openai or CREDENCE_LLM_PROVIDER=anthropic for API-based models.
Key Results
| Agent | Score | Accuracy | Tools/Q |
|---|---|---|---|
| oracle | +188.2 | 70.6% | 1.08 |
| bayesian | +112.6 | 59.6% | 0.99 |
| langchain_react | -7.4 | 64.0% | 3.22 |
| langchain_enhanced | -68.2 | 66.0% | 3.94 |
The Bayesian agent outscores LangChain by 120 points despite lower accuracy — it queries ~1 tool per question instead of ~3.2, and strategically abstains on low-confidence questions. Enhanced prompting makes LangChain worse by triggering more tool calls without proportional accuracy gains.
See results/RESULTS.md for full results across all three
experiments (stationary, drift, ablation).
Project Structure
credence/
├── credence/ # Facade package — public API re-exports
│ └── __init__.py
├── src/
│ ├── inference/ # Domain-agnostic Bayesian inference layer
│ │ ├── beta_posterior.py # Beta-Bernoulli reliability tracking
│ │ ├── voi.py # Value of information, ScoringRule, ToolConfig
│ │ └── decision.py # EU-based decision logic
│ ├── agents/
│ │ ├── bayesian_agent.py # Domain-agnostic Bayesian agent
│ │ ├── common.py # Shared agent interface
│ │ ├── baselines.py # Random, all-tools, oracle agents
│ │ ├── langchain_agent.py # Standard LangChain ReAct agent
│ │ └── langchain_enhanced.py # LangChain with best-effort prompting
│ ├── environment/ # Benchmark-specific: simulated tools and questions
│ │ ├── benchmark.py # The benchmark harness
│ │ ├── tools.py # Simulated tools with known reliability
│ │ ├── questions.py # Question bank with ground truth
│ │ └── categories.py # Category definitions, make_keyword_category_infer_fn
│ ├── analysis/
│ │ ├── metrics.py # Score, calibration, cost metrics
│ │ └── visualisation.py # Plots and dashboards
│ └── utils/
│ └── logging.py # Structured logging for analysis
├── tests/
├── experiments/
│ ├── run_stationary.py # Main experiment: stationary reliabilities
│ ├── run_drift.py # Extension: tool reliability drift
│ └── run_ablation.py # Ablation studies
├── results/ # Generated plots and data
└── pyproject.toml # Core deps vs [benchmark] vs [dev] extras
Design Principles
- Everything is expected utility maximisation — no heuristics
- No hacks — if it doesn't work, fix the model
- LLM outputs are data — with quantified uncertainty
- The benchmark must be fair — LangChain gets every advantage
- Be honest about parameters — every number is justified
See CLAUDE.md for architecture and development guidelines.
See SPEC.md for the full mathematical specification.
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