Non-Equilibrium Relations for Bounded Rational Decision-Making in Changing Environments

Jarzyski's Equality and Crooks' Fluctuation Theorem for General Markov Chains with Application to Decision-Making Systems

We define common thermodynamic concepts purely within the framework of general Markov chains and derive Jarzynski's equality and Crooks' fluctuation theorem in this setup. In particular, we regard the discrete-time case, which leads to an asymmetry in the definition of work that appears in the usual formulation of Crooks' fluctuation theorem. We show how this asymmetry can be avoided with an additional condition regarding the energy protocol. The general formulation in terms of Markov chains allows transferring the results to other application areas outside of physics. Here, we discuss how this framework can be applied in the context of decision-making. This involves the definition of the relevant quantities, the assumptions that need to be made for the different fluctuation theorems to hold, as well as the consideration of discrete trajectories instead of the continuous trajectories, which are relevant in physics.

Optimal evolutionary decision-making to store immune memory

The adaptive immune system provides a diverse set of molecules that can mount specific responses against a multitude of pathogens. Memory is a key feature of adaptive immunity, which allows organisms to respond more readily upon re-infections. However, differentiation of memory cells is still one of the least understood cell fate decisions. Here, we introduce a mathematical framework to characterize optimal strategies to store memory to maximize the utility of immune response over an organism's lifetime. We show that memory production should be actively regulated to balance between affinity and cross-reactivity of immune receptors for an effective protection against evolving pathogens. Moreover, we predict that specificity of memory should depend on the organism's lifespan, and shorter lived organisms with fewer pathogenic encounters should store more cross-reactive memory. Our framework provides a baseline to gauge the efficacy of immune memory in light of an organism's coevolutionary history with pathogens.

Specialization in Hierarchical Learning Systems

Joining multiple decision-makers together is a powerful way to obtain more sophisticated decision-making systems, but requires to address the questions of division of labor and specialization. We investigate in how far information constraints in hierarchies of experts not only provide a principled method for regularization but also to enforce specialization. In particular, we devise an information-theoretically motivated on-line learning rule that allows partitioning of the problem space into multiple sub-problems that can be solved by the individual experts. We demonstrate two different ways to apply our method: (i) partitioning problems based on individual data samples and (ii) based on sets of data samples representing tasks. Approach (i) equips the system with the ability to solve complex decision-making problems by finding an optimal combination of local expert decision-makers. Approach (ii) leads to decision-makers specialized in solving families of tasks, which equips the system with the ability to solve meta-learning problems. We show the broad applicability of our approach on a range of problems including classification, regression, density estimation, and reinforcement learning problems, both in the standard machine learning setup and in a meta-learning setting.