What is Active Inference?

Active Inference is a theoretical framework from neuroscience, derived from Karl Friston's Free Energy Principle (FEP). It proposes that all biological agents (including brains) work by minimizing "surprise" - the difference between what they expect and what they observe.

How It Applies to Trading

In trading, the agent (our model) tries to predict future market states and takes actions (trades) that both:

• 1.Exploit - Take profitable positions based on confident beliefs
• 2.Explore - Gather information to reduce uncertainty (epistemic value)

The model balances profit-seeking with information-gathering through Expected Free Energy (EFE) minimization, weighted by an epistemic parameter (EPISTEMIC_WEIGHT). This is fundamentally different from reinforcement learning which only optimizes for reward.

Why Different from Traditional Quant Methods?

Partially Observable Markov Decision Process

A POMDP is a mathematical framework for decision-making under uncertainty. Unlike MDPs where the state is fully known, in POMDPs the agent must infer the hidden state from noisy observations - perfect for financial markets where the true "regime" is never directly visible.

       POMDP Structure for Trading
       ============================

    ┌─────────────────────────────────────────────────────────┐
    │                    HIDDEN STATES                         │
    │         (Market Regimes x Position States)               │
    │                                                          │
    │   ┌─────────┐   ┌─────────┐   ┌─────────┐   ┌─────────┐ │
    │   │ Bullish │   │Neutral-U│   │Neutral-D│   │ Bearish │ │
    │   └────┬────┘   └────┬────┘   └────┬────┘   └────┬────┘ │
    └────────┼─────────────┼─────────────┼─────────────┼──────┘
             │             │             │             │
             ▼             ▼             ▼             ▼
    ┌─────────────────────────────────────────────────────────┐
    │                    OBSERVATIONS                          │
    │              (What the model "sees")                     │
    │                                                          │
    │  ┌────────┐ ┌────────┐ ┌────────┐ ┌────────┐ ┌────────┐ │
    │  │ Return │ │  P&L   │ │Momentum│ │  Vol   │ │VolShock│ │
    │  │ (4bin) │ │ (4bin) │ │ (3bin) │ │ (3bin) │ │ (2bin) │ │
    │  └────────┘ └────────┘ └────────┘ └────────┘ └────────┘ │
    │                                                          │
    │      Total: 4 x 4 x 3 x 3 x 2 = 288 observation combos   │
    └─────────────────────────────────────────────────────────┘
             │
             ▼
    ┌─────────────────────────────────────────────────────────┐
    │                     ACTIONS                              │
    │              (Position Changes)                          │
    │                                                          │
    │          ┌──────┐  ┌──────┐  ┌──────┐                   │
    │          │ LONG │  │ FLAT │  │ SHORT│                   │
    │          └──────┘  └──────┘  └──────┘                   │
    └─────────────────────────────────────────────────────────┘

The 5 Core Matrices (A, B, C, D, E)

The POMDP is defined by five matrices that encode the model's beliefs about the world:

Confidence Gating: The Dual Threshold System

The model only executes trades when it passes two independent confidence gates. This prevents trading on weak signals.

Position Sizing: Kelly Criterion

Once a trade signal passes both gates, the model uses the Kelly Criterion to determine position size - the mathematically optimal fraction of capital to bet.

We use Half-Kelly which reduces position sizes by 50% compared to theoretical optimum. This sacrifices some expected return for significantly reduced volatility and drawdown risk.

Loss Aversion: Behavioral Finance Integration

Drawing from Kahneman and Tversky's Prospect Theory, the model weights losses more heavily than gains. This reflects how real traders and investors actually behave - and helps preserve capital.

With LOSS_AVERSION = 2.25, a $100 loss feels 2.25x worse than a $100 gain feels good. This asymmetry makes the model naturally risk-averse and helps avoid catastrophic drawdowns.

Training the Generative Model

Unlike neural networks that learn through backpropagation, Active Inference models learn through Bayesian belief updating. Each model maintains Dirichlet concentration parameters over its 5-modality observation matrix (A), trained on Jan 2015 - Dec 2025 historical data. The training loop processes each day sequentially: observe market features, infer hidden state, evaluate policies via Expected Free Energy, select action, then update A[0] concentrations.

    Training Pipeline
    =================

    Historical Data (2015-2025)
           │
           ▼
    ┌──────────────────┐
    │  Feature Engine  │ ──► Returns, Momentum, Vol, VolumeShock
    └────────┬─────────┘
             │
             ▼
    ┌──────────────────┐
    │  Discretization  │ ──► Convert continuous → discrete bins
    └────────┬─────────┘
             │
             ▼
    ┌──────────────────┐     ┌─────────────────────────────────┐
    │   POMDP Agent    │ ◄───│  Dirichlet Concentration Prior  │
    │                  │     │  A[0]: 20x (learnable)          │
    │  For each day:   │     │  A[1-4]: 1000x (frozen domain)  │
    │  1. Observe      │     └─────────────────────────────────┘
    │  2. Infer state  │
    │  3. Select policy│
    │  4. Update A     │
    └────────┬─────────┘
             │
             ▼
    ┌──────────────────┐
    │  Trained Model   │ ──► HMAC-signed, versioned, stored
    └──────────────────┘

Online Learning: Dirichlet Updates

After training, each model continues to learn daily using Dirichlet concentration updates. Only modality A[0] (returns observation model, concentration=20x) is updated; modalities A[1-4] (P&L, momentum, volatility, volume shock) remain frozen at 1000x concentration to preserve domain knowledge.

Model Versioning & A/B Testing

Every trained model is cryptographically signed with HMAC-SHA256 using a secret key. This ensures model integrity and enables reproducible research.

Multiple model versions can run simultaneously (e.g., SPY_conservative, SPY_aggressive) to A/B test different parameter configurations in live paper trading.

Why Metrics Show "--"

You'll see dashes in metrics when there's insufficient data to calculate them reliably:

Paper Trading vs Backtesting vs Live