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# catopt-category-theoretic-compositional- # CatOpt: Category-Theoretic Compositional Optimizer (MVP)
Problem space: distributed, offline-first optimization across heterogeneous edge devices (DERs, meters, controllers, EV chargers) in mesh networks. Centralized solvers are infeasible due to latency, bandwidth, and privacy. We need a modular, provably compositional optimization framework that can be plugged into existing energy and robotics ecosystems with privacy by design and offline resilience. CatOpt is a lightweight, open-source framework for privacy-preserving, compositional distributed optimization across edge meshes. The MVP emphasizes a minimal, well-structured surface built on category-theory abstractions, enabling edge-to-edge collaboration with offline resilience and vendor interoperability.
This repository implements a minimal MVP scaffold for CatOpt, a light-weight framework that uses category-theory-inspired abstractions to express distributed optimization problems and a toy solver stack to validate the idea in CI. What you get in this MVP
- Local problems expressed by agents (objects)
- Data exchange channels (morphisms) and problem transformers (functors)
- Global assembly via Limits/Colimits and a lightweight ADMM-like solver
- Privacy-by-design data contracts and modular adapters
- A tiny Python runtime surface suitable for rapid prototyping and CI validation
MVP Runtime (new): lightweight primitives to experiment with CatOpt concepts locally. Why this matters
- LocalProblem: representation of an agent's optimization task. - Composability: add/remove agents without re-deriving the global problem
- DataContract, SharedVariables, PlanDelta: lightweight data-exchange primitives for a privacy-conscious mesh. - Privacy: only exchanged, abstracted quantities per contracts
- ADMMTwoAgentSolver: tiny, in-process ADMM-like solver to demonstrate joint optimization across two agents. - Convergence: disciplined, modular solver structure with verifiable properties
- demo_two_agent_admm(): quick in-repo demonstration function returning final variables. - Interoperability: bridges to existing energy/robotics ecosystems via a common DSL
Usage notes: Usage (quick start)
- Import from the package and optionally run the demo function to observe convergence on a toy problem. - The core runtime primitives live in src/catopt_category_theoretic_compositional_/
- Example: - The tiny DSL bridge to contracts lives in src/catopt_category_theoretic_compositional_/dsl.py
```python - Importing and testing is kept simple to satisfy the CI gate (see tests/test_basic.py)
from catopt_category_theoretic_compositional.runtime import ADMMTwoAgentSolver, demo_two_agent_admm
result = demo_two_agent_admm() For more details, see tests, the MVP runtime, and the protocol DSL (ProtocolContract, build_minimal_contract).
print(result)
``` This README is a starting point. As we evolve, we will add more examples, adapters, and end-to-end demos.

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"""CatOpt: Minimal placeholder surface & MVP runtime exposure.""" """CatOpt: Minimal placeholder surface & MVP runtime exposure."""
from .runtime import LocalProblem, SharedVariables, DataContract, PlanDelta, ADMMTwoAgentSolver, demo_two_agent_admm # noqa: F401 from .runtime import LocalProblem, SharedVariables, DataContract, PlanDelta, ADMMTwoAgentSolver, demo_two_agent_admm # noqa: F401
from .dsl import ProtocolContract, build_minimal_contract # noqa: F401
def add(a: int, b: int) -> int: def add(a: int, b: int) -> int:
"""Return the sum of two integers. """Return the sum of two integers.
@ -10,4 +11,14 @@ def add(a: int, b: int) -> int:
""" """
return a + b return a + b
__all__ = ["add", "LocalProblem", "SharedVariables", "DataContract", "PlanDelta", "ADMMTwoAgentSolver", "demo_two_agent_admm"] __all__ = [
"add",
"LocalProblem",
"SharedVariables",
"DataContract",
"PlanDelta",
"ADMMTwoAgentSolver",
"demo_two_agent_admm",
"ProtocolContract",
"build_minimal_contract",
]

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"""CatOpt Minimal Protocol DSL
Lightweight protocol primitives to express a minimal, vendor-agnostic
contract between agents in the CatOpt MVP. This module is intentionally
small and proto-like to avoid pulling in heavy dependencies while still
providing a useful representation that can be serialized for transport.
"""
from __future__ import annotations
from dataclasses import dataclass, field
from typing import Dict, List
import json
from .runtime import LocalProblem, DataContract, SharedVariables
@dataclass
class ProtocolContract:
"""A minimal, JSON-serializable contract describing the exchange schema."""
version: int = 1
objects: List[Dict] = field(default_factory=list)
morphisms: List[Dict] = field(default_factory=list)
functors: List[Dict] = field(default_factory=list)
limits: List[Dict] = field(default_factory=list)
time_structure: Dict = field(default_factory=lambda: {"monoid": "temporal", "rounds": 1})
def to_dict(self) -> Dict:
return {
"version": self.version,
"objects": self.objects,
"morphisms": self.morphisms,
"functors": self.functors,
"limits": self.limits,
"time_structure": self.time_structure,
}
def to_json(self) -> str:
return json.dumps(self.to_dict(), indent=2, sort_keys=True)
def build_minimal_contract(lp: LocalProblem, dc: DataContract, sv: SharedVariables) -> ProtocolContract:
"""Construct a tiny, canonical contract from local problem state.
This is intentionally small but demonstrates how a solver could export a
structured contract for cross-agent interoperability.
"""
obj = {
"type": "LocalProblem",
"id": lp.id,
"x_name": lp.x_name,
"objective": {
"quadratic": lp.a,
"linear": lp.b,
},
}
contract = ProtocolContract(
version=1,
objects=[obj],
morphisms=[{"from": "agentA", "to": "agentB", "contract": "delta-sharing"}],
functors=[{"name": "Canonicalize", "description": "maps to vendor-agnostic representation"}],
limits=[{"type": "global-constraint", "description": "sum(x) == 1"}],
time_structure={"monoid": "temporal", "rounds": 1},
)
return contract