The study of intelligent systems explains behaviour in terms of economic
rationality. This results in an optimization principle involving a function or
utility, which states that the system will evolve until the configuration of
maximum utility is achieved. Recently, this theory has incorporated
constraints, i.e., the optimum is achieved when the utility is maximized while
respecting some information-processing constraints. This is reminiscent of
thermodynamic systems. As such, the study of intelligent systems has benefited
from the tools of thermodynamics. The first aim of this thesis is to clarify
the applicability of these results in the study of intelligent systems.
We can think of the local transition steps in thermodynamic or intelligent
systems as being driven by uncertainty. In fact, the transitions in both
systems can be described in terms of majorization. Hence, real-valued
uncertainty measures like Shannon entropy are simply a proxy for their more
involved behaviour. More in general, real-valued functions are fundamental to
study optimization and complexity in the order-theoretic approach to several
topics, including economics, thermodynamics, and quantum mechanics. The second
aim of this thesis is to improve on this classification.
The basic similarity between thermodynamic and intelligent systems is based
on an uncertainty notion expressed by a preorder. We can also think of the
transitions in the steps of a computational process as a decision-making
procedure. In fact, by adding some requirements on the considered order
structures, we can build an abstract model of uncertainty reduction that allows
to incorporate computability, that is, to distinguish the objects that can be
constructed by following a finite set of instructions from those that cannot.
The third aim of this thesis is to clarify the requirements on the order
structure that allow such a framework.

研究智能系统以经济合理性解释其行为，其中包括涉及函数或效用的优化原则，最近这一理论已将约束纳入进来，即在满足某些信息处理约束的同时最大化效用。研究智能系统已从热力学工具中受益，本篇论文的目标是澄清这些结果在研究智能系统中的适用性，并改善对排序结构的分类和对能够允许这样的框架的要求的理解。

决策的排序模型：学习、优化、复杂性和计算

Order-theoretic models for decision-making: Learning, optimization,  complexity and computation

What computational principles underlie human pragmatic reasoning? A prominent
approach to pragmatics is the Rational Speech Act (RSA) framework, which
formulates pragmatic reasoning as probabilistic speakers and listeners
recursively reasoning about each other. While RSA enjoys broad empirical
support, it is not yet clear whether the dynamics of such recursive reasoning
may be governed by a general optimization principle. Here, we present a novel
analysis of the RSA framework that addresses this question. First, we show that
RSA recursion implements an alternating maximization for optimizing a tradeoff
between expected utility and communicative effort. On that basis, we study the
dynamics of RSA recursion and disconfirm the conjecture that expected utility
is guaranteed to improve with recursion depth. Second, we show that RSA can be
grounded in Rate-Distortion theory, while maintaining a similar ability to
account for human behavior and avoiding a bias of RSA toward random utterance
production. This work furthers the mathematical understanding of RSA models,
and suggests that general information-theoretic principles may give rise to
human pragmatic reasoning.

本文研究了何种计算原则支持人类实用推理。使用 RSA 框架，论文以概率说话者和听者递归推理为基础，分析了 RSA 递归推理动力学，并探讨了相关的信息理论原则，以实现优化实用程序和交际努力的平衡。