Regression and progression in stochastic domains

Abstract

Reasoning about degrees of belief in uncertain dynamic worlds is fundamental to many applications, such as robotics and planning, where actions modify state properties and sensors provide measurements, both of which are prone to noise. With the exception of limited cases such as Gaussian processes over linear phenomena, belief state evolution can be complex and hard to reason with in a general way, especially when the agent has to deal with categorical assertions, incomplete information such as disjunctive knowledge, as well as probabilistic knowledge. Among the many approaches for reasoning about degrees of belief in the presence of noisy sensing and acting, the logical account proposed by Bacchus, Halpern, and Levesque is perhaps the most expressive, allowing for such belief states to be expressed naturally as constraints. While that proposal is powerful, the task of how to plan effectively is not addressed. In fact, at a more fundamental level, the task of projection, that of reasoning about beliefs effectively after acting and sensing, is left entirely open. To aid planning algorithms, we study the projection problem in this work. In the reasoning about actions literature, there are two main solutions to projection: regression and progression. Both of these have proven enormously useful for the design of logical agents, essentially paving the way for cognitive robotics. Roughly, regression reduces a query about the future to a query about the initial state. Progression, on the other hand, changes the initial state according to the effects of each action and then checks whether the formula holds in the updated state. In this work, we show how both of these generalize in the presence of degrees of belief, noisy acting and sensing. Our results allow for both discrete and continuous probability distributions to be used in the specification of beliefs and dynamics.

Logic + probabilistic programming + causal laws

“…So we need to incorporate these read values to ascertain if the program terminates. 2 The semantical foundations of ALLEGRO incorporating these ideas was established in [11] with a discussion on its empirical behaviour.…”

“…-HYPE [9]: a planning framework based on distributional clauses [10]; and -ALLEGRO [11]: a high-level control programming framework that extends GOLOG [12]. These two systems emphasize different strengths of probabilistic programming, which we think are particularly useful for complex modelling issues raised in probabilistic planning.…”

“…Among other things, one can instantiate planning problems with growing and shrinking state spaces, discrete and continuous probability distributions, and non-unique prior distributions in a first-order setting. More precisely, we provide an overview of the features of two systems: HYPE [ 9 ]: a planning framework based on distributional clauses [ 10 ]; and ALLEGRO [ 11 ]: a high-level control programming framework that extends GOLOG [ 12 ]. These two systems emphasize different strengths of probabilistic programming, which we think are particularly useful for complex modelling issues raised in probabilistic planning.…”

On the Progression of Belief

“…For a limited type of theory, the progression of discrete degrees of belief wrt context-completeness is considered in (Belle and Lakemeyer 2011). Belle and Levesque (2020) studied the progression of continuous degrees of belief for the so called invertible BATs which exclude our BATs in Example 2. As a result, our work fills the gap of a general account of progression in discrete degrees of belief.…”

General Policies, Representations, and Planning Width

“…In this work, we address these and related questions. For this, we bring the notion of general policies; policies that solve multiple instances of a planning domain all at once (Srivastava, Immerman, & Zilberstein, 2008;Bonet & Geffner, 2015;Hu & De Giacomo, 2011;Belle & Levesque, 2016;Segovia, Jiménez, & Jonsson, 2016), while using the formulation of general policies expressed in terms of finite sets of rules over a fixed set of Boolean and numerical features (Bonet & Geffner, 2018).…”