@waldzellai/stochasticthinking/README.md

MCP server for stochastic algorithms and probabilistic decision making

# Stochastic Thinking MCP Server

[![smithery badge](https://smithery.ai/badge/@waldzellai/stochasticthinking)](https://smithery.ai/server/@waldzellai/stochasticthinking)

## Why Stochastic Thinking Matters

When AI assistants make decisions - whether writing code, solving problems, or suggesting improvements - they often fall into patterns of "local thinking", similar to how we might get stuck trying the same approach repeatedly despite poor results. This is like being trapped in a valley when there's a better solution on the next mountain over, but you can't see it from where you are.

This server introduces advanced decision-making strategies that help break out of these local patterns:
- Instead of just looking at the immediate next step (like basic Markov chains do), these algorithms can look multiple steps ahead and consider many possible futures
- Rather than always picking the most obvious solution, they can strategically explore alternative approaches that might initially seem suboptimal
- When faced with uncertainty, they can balance the need to exploit known good solutions with the potential benefit of exploring new ones

Think of it as giving your AI assistant a broader perspective - instead of just choosing the next best immediate action, it can now consider "What if I tried something completely different?" or "What might happen several steps down this path?"

A Model Context Protocol (MCP) server that provides stochastic algorithms and probabilistic decision-making capabilities, extending the sequential thinking server with advanced mathematical models.

## Features

### Stochastic Algorithms

#### Markov Decision Processes (MDPs)
- Optimize policies over long sequences of decisions
- Incorporate rewards and actions
- Support for Q-learning and policy gradients
- Configurable discount factors and state spaces

#### Monte Carlo Tree Search (MCTS)
- Simulate future action sequences
- Balance exploration and exploitation
- Configurable simulation depth and exploration constants
- Ideal for large decision spaces

#### Multi-Armed Bandit Models
- Balance exploration vs exploitation
- Support multiple strategies:
  - Epsilon-greedy
  - UCB (Upper Confidence Bound)
  - Thompson Sampling
- Dynamic reward tracking

#### Bayesian Optimization
- Optimize decisions with uncertainty
- Probabilistic inference models
- Configurable acquisition functions
- Continuous parameter optimization

#### Hidden Markov Models (HMMs)
- Infer latent states
- Forward-backward algorithm
- State sequence prediction
- Emission probability modeling

## Usage

### Installation

#### Installing via Smithery

To install Stochastic Thinking MCP Server for Claude Desktop automatically via [Smithery](https://smithery.ai/server/@waldzellai/stochasticthinking):

```bash
npx -y @smithery/cli install @waldzellai/stochasticthinking --client claude
```

#### Manual Installation
```bash
npm install @waldzellai/stochasticthinking
```

Or run with npx:

```bash
npx @waldzellai/stochasticthinking
```

### API Examples

#### Markov Decision Process
```typescript
const response = await mcp.callTool("stochasticalgorithm", {
  algorithm: "mdp",
  problem: "Optimize robot navigation policy",
  parameters: {
    states: 100,
    actions: ["up", "down", "left", "right"],
    gamma: 0.9,
    learningRate: 0.1
  }
});
```

#### Monte Carlo Tree Search
```typescript
const response = await mcp.callTool("stochasticalgorithm", {
  algorithm: "mcts",
  problem: "Find optimal game moves",
  parameters: {
    simulations: 1000,
    explorationConstant: 1.4,
    maxDepth: 10
  }
});
```

#### Multi-Armed Bandit
```typescript
const response = await mcp.callTool("stochasticalgorithm", {
  algorithm: "bandit",
  problem: "Optimize ad placement",
  parameters: {
    arms: 5,
    strategy: "epsilon-greedy",
    epsilon: 0.1
  }
});
```

#### Bayesian Optimization
```typescript
const response = await mcp.callTool("stochasticalgorithm", {
  algorithm: "bayesian",
  problem: "Hyperparameter optimization",
  parameters: {
    acquisitionFunction: "expected_improvement",
    kernel: "rbf",
    iterations: 50
  }
});
```

#### Hidden Markov Model
```typescript
const response = await mcp.callTool("stochasticalgorithm", {
  algorithm: "hmm",
  problem: "Infer weather patterns",
  parameters: {
    states: 3,
    algorithm: "forward-backward",
    observations: 100
  }
});
```

## Algorithm Selection Guide

Choose the appropriate algorithm based on your problem characteristics:

### Markov Decision Processes (MDPs)
Best for:
- Sequential decision-making problems
- Problems with clear state transitions
- Scenarios with defined rewards
- Long-term optimization needs

### Monte Carlo Tree Search (MCTS)
Best for:
- Game playing and strategic planning
- Large decision spaces
- When simulation is possible
- Real-time decision making

### Multi-Armed Bandit
Best for:
- A/B testing
- Resource allocation
- Online advertising
- Quick adaptation needs

### Bayesian Optimization
Best for:
- Hyperparameter tuning
- Expensive function optimization
- Continuous parameter spaces
- When uncertainty matters

### Hidden Markov Models (HMMs)
Best for:
- Time series analysis
- Pattern recognition
- State inference
- Sequential data modeling

## Development

1. Clone the repository
2. Install dependencies: `npm install`
3. Build the project: `npm run build`
4. Start the server: `npm start`

## Contributing

Contributions are welcome! Please feel free to submit a Pull Request.

## License

MIT License - see LICENSE for details.

## Acknowledgments

- Based on the Model Context Protocol (MCP) by Anthropic
- Extends the sequential thinking server with stochastic capabilities
- Inspired by classic works in reinforcement learning and decision theory