Information theoretic approach to interactive learning

The principles of statistical mechanics and information theory play an important role in learning and have inspired both theory and the design of numerous machine learning algorithms. The new aspect in this paper is a focus on integrating feedback from the learner. A quantitative approach to interactive learning and adaptive behavior is proposed, integrating model- and decision-making into one theoretical framework. This paper follows simple principles by requiring that the observer’s world model and action policy should result in maximal predictive power at minimal complexity. Classes of optimal action policies and of optimal models are derived from an objective function that reflects this trade-off between prediction and complexity. The resulting optimal models then summarize, at different levels of abstraction, the process’s causal organization in the presence of the learner’s actions. A fundamental consequence of the proposed principle is that the learner’s optimal action policies balance exploration and control as an emerging property. Interestingly, the explorative component is present in the absence of policy randomness, i.e. in the optimal deterministic behavior. This is a direct result of requiring maximal predictive power in the presence of feedback.

💡 Research Summary

The paper proposes a unified information‑theoretic framework for interactive learning in which a learner’s actions feed back into the environment and consequently influence the learner’s own model. Building on the well‑established connections between statistical mechanics, information theory, and machine‑learning, the authors introduce a single principle: the learner should maximize predictive power while minimizing the complexity of both its internal world model and its action policy.

Formally, the learner is described by three random variables: past observations and actions ((x_{<t},a_{<t})), an internal state (z_t) that serves as a sufficient statistic for the future, and the next action (a_t). The future observation (x_{t+1}) is predicted by the conditional distribution (p(x_{t+1}\mid z_t,a_t)). The objective function is

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