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- Source: inbox/archive/2020-12-00-da-costa-active-inference-discrete-state-spaces.md - Domain: ai-alignment - Extracted by: headless extraction cron (worker 3) Pentagon-Agent: Theseus <HEADLESS>
45 lines
3.3 KiB
Markdown
45 lines
3.3 KiB
Markdown
---
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type: claim
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domain: ai-alignment
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secondary_domains: [critical-systems]
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description: "Expected free energy subsumes information gain, expected utility, and risk-sensitivity as special cases of a single objective function"
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confidence: likely
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source: "Da Costa et al. (2020), Journal of Mathematical Psychology - Active Inference on Discrete State-Spaces: A Synthesis"
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url: "https://www.sciencedirect.com/science/article/pii/S0022249620300857"
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arxiv: "https://arxiv.org/abs/2001.07203"
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created: 2026-03-11
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depends_on: []
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challenged_by: []
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---
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# Active inference unifies perception, action, planning, and learning under free energy minimization where expected free energy subsumes information gain, expected utility, and risk-sensitivity as special cases
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Active inference provides a unified mathematical framework for intelligent behavior by postulating that agents optimize two complementary objective functions:
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1. **Variational free energy (VFE)** measures the fit between an internal model and past sensory observations (retrospective inference)
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2. **Expected free energy (EFE)** scores possible future courses of action in relation to prior preferences (prospective planning)
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The key theoretical contribution is that expected free energy subsumes many existing constructs in science and engineering as special cases. Da Costa et al. (2020) formally demonstrate that EFE includes:
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- **Information gain** (epistemic value): The reduction in uncertainty about the environment
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- **Expected utility** (pragmatic value): The alignment of outcomes with agent preferences
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- **KL-control** (risk-sensitivity): The penalty for diverging from a baseline policy
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This unification means active inference doesn't replace existing frameworks for decision-making and planning—it provides the mathematical foundation that shows how they relate to each other under a single coherent objective function. The paper states: "The most likely courses of action taken by those systems are those which minimise expected free energy."
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The discrete-state formulation is particularly relevant for systems where states, actions, and observations can be enumerated (like knowledge graphs, claim networks, or research direction selection). In these domains, the framework provides tractable algorithms for perception, action selection, planning, and learning under a single objective.
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## Evidence
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- Da Costa et al. (2020) provides formal mathematical derivations showing how information gain, expected utility, and risk-sensitivity emerge as special cases of EFE minimization
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- The paper is a comprehensive tutorial published in the Journal of Mathematical Psychology covering the complete discrete-state formulation
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- The framework explicitly covers perception, action, planning, decision-making, and learning as unified under free energy minimization
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- The mathematical proofs demonstrate that agents minimizing EFE implicitly optimize for both epistemic value (learning) and pragmatic value (goal achievement)
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---
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Relevant Notes:
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- [[safe AI development requires building alignment mechanisms before scaling capability]]
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- [[coordination protocol design produces larger capability gains than model scaling because the same AI model performed 6x better with structured exploration than with human coaching on the same problem]]
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Topics:
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- [[domains/ai-alignment/_map]]
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- [[foundations/critical-systems/_map]]
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