The motivations for acting and planning with probabilistic models are about handling uncertainty in a quantitative way, with optimal or near-optimal decisions. The future is never entirely and precisely predictable. Uncertainty can be due to exogenous events in the environment, from nature and other actors, to noisy sensing and information gathering actions, to possible failures and outcomes of imprecise or intrinsically nondeterministic actions. Models are necessarily incomplete. Knowledge about open environments is partial. Part of what may happen can be only be modeled with uncertainty. Even in closed predictable environments, complete deterministic models may be too complex to develop. The three chapters in Part III tackle acting, planning, and learning in a probabilistic setting.

This chapter is about planning techniques for solving MDP problems. It presents algorithms that seeks optimal or near-optimal solution policies for a domain. Most of the chapter is focused on indefinite-horizon goal reachability domains that have positive costs and a safe solution; they may have dead ends, but those are avoidable. The chapter presents dynamic programming algorithms, heuristics search methods and their heuristics, linear programming methods, and online and Monte Carlo tree search techniques.

In probabilistic models, an action can have several possible outcomes that are not equally likely; their distribution can be estimated relying on statistics of past observations. The purpose is to act optimally with respect to an optimization criterion of the estimated likelihood of action effects and their cost. The usual formal probabilistic models are Markov decision processes (MDPs). An MDP is a nondeterministic state-transition system with a probability distribution and a cost distribution. The probability distribution defines how likely it is to get to a state 𝑠′ when an action 𝑎 is performed in a state 𝑠. The chapter presents MDPs in flat then structured state-space representations. Section 8.3 covers modeling issues of a probabilistic domain with MDPs and variants such as the stochastic shortest path model (SSP) or the constrained MDP (C-MDP) model. Section 8.4 focuses on acting with MDPs. Partially observable MDPs and other extended models are discussed in Section 8.5.

This chapter is about a refinement acting engine (RAE) used on a hierarchical task-oriented representation. It relies on an expressive, general-purpose language that offers rich programming control structures for online decision-making. A collection of refinement methods describes alternative ways to handle tasks and react to events. A method can be any complex algorithm, decomposing a task into subtasks and primitive actions. Subtasks are refined recursively. Nondeterministic actions trigger sensory-motor procedures that query and change the world nondeterministically. We assume that the methods are manually specified and that RAE chooses the appropriate method for the task and context at hand heuristically.

The recent developments of large language models (LLMs) and their extension in multimodal foundation models have introduced new perspectives in AI. An LLM is basically a very large neural net trained as a statistical predictor of the likely continuation of a sequence of words. LLMs have excellent competencies over a broad set of NLP tasks. Additionally, LLMs demonstrate the emergence of deliberation capabilities for reasoning, common sense, problem solving, code writing, and planning. These abilities have not been designed for in LLMs. They are unexpected and remain to a large extent poorly understood. Although error-prone and imperfect, they open up promising perspectives for acting, planning, and learning, which are presented in this chapter.

This chapter is about domain-independent classical-planning algorithms, which until recently were the most widely studied class of AI planning algorithms. The chapter classifies and describes a variety of forward search, backward search, and plan-space planning algorithms, as well as heuristics for guiding the algorithms.