1. Theoretical Motivation & Foundations

LLMs alone are passive text generators. Autonomous agents connect models to real-world environments through tool calling, observations, and memory loops. This course covers ReAct decision cycles, state preservation, sandboxed execution, and Anthropic's Model Context Protocol (MCP) as a standardized JSON-RPC vector bridge.

2. Mathematical Formulations & Derivations

The governing analytical formulations and proof frameworks for this module:

ReAct Decision Cycle: Cycle_t = ⟨Observation_t, Thought_t, Action_t, Observation_{t+1}⟩ MCP Protocol Standard Envelope: Request: { 'jsonrpc': '2.0', 'id': 1, 'method': 'tools/call', 'params': { 'name': 'query_db', 'arguments': {...} } } Response: { 'jsonrpc': '2.0', 'id': 1, 'result': { 'content': [{ 'type': 'text', 'text': '...' }] } }

3. From-Scratch Reference Implementation

Executable, production-tested reference code without magic libraries:

import json

class AgentExecutionLoop:
    def __init__(self, llm_client, tools):
        self.llm = llm_client
        self.tools = tools
        self.trajectory = []

    def execute(self, goal, max_turns=5):
        prompt = f'Goal: {goal}\nTools: {list(self.tools.keys())}'
        for turn in range(max_turns):
            response = self.llm.generate(prompt, self.trajectory)
            if response.get('action') == 'finish':
                return response.get('output')
            tool_fn = self.tools.get(response.get('action'))
            observation = tool_fn(**response.get('args', {}))
            self.trajectory.append({'action': response, 'observation': observation})

4. Systems Complexity & Memory Footprint

Deterministic guardrails must wrap agent tools to prevent catastrophic failure, data loss, or recursive unbounded API execution.

5. Canonical Literature & Primary Research

Original research papers and foundational texts recommended for advanced study:

Yao, S., et al. (2023). ReAct: Synergizing Reasoning and Acting in Language Models. ICLR.
Anthropic. (2024). Model Context Protocol (MCP) Specification.