Improving Connectionist Energy Minimization

Symmetric networks designed for energy minimization such as Boltzman machines and Hopfield nets are frequently investigated for use in optimization, constraint satisfaction and approximation of NP-hard problems. Nevertheless, finding a global solution (i.e., a global minimum for the energy function) is not guaranteed and even a local solution may take an exponential number of steps. We propose an improvement to the standard local activation function used for such networks. The improved algorithm guarantees that a global minimum is found in linear time for tree-like subnetworks. The algorithm, called activate, is uniform and does not assume that the network is tree-like. It can identify tree-like subnetworks even in cyclic topologies (arbitrary networks) and avoid local minima along these trees. For acyclic networks, the algorithm is guaranteed to converge to a global minimum from any initial state of the system (self-stabilization) and remains correct under various types of schedulers. On the negative side, we show that in the presence of cycles, no uniform algorithm exists that guarantees optimality even under a sequential asynchronous scheduler. An asynchronous scheduler can activate only one unit at a time while a synchronous scheduler can activate any number of units in a single time step. In addition, no uniform algorithm exists to optimize even acyclic networks when the scheduler is synchronous. Finally, we show how the algorithm can be improved using the cycle-cutset scheme. The general algorithm, called activate-with-cutset, improves over activate and has some performance guarantees that are related to the size of the network's cycle-cutset.Comment: See http://www.jair.org/ for any accompanying file

Deep Learning with Logical Constraints

In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be compliant with the background knowledge itself, e.g., for safety-critical applications. In this survey, we retrace such works and categorize them based on (i) the logical language that they use to express the background knowledge and (ii) the goals that they achieve.Comment: Survey paper. IJCAI 202

PDDL2.1: An extension of PDDL for expressing temporal planning domains

In recent years research in the planning community has moved increasingly towards application of planners to realistic problems involving both time and many types of resources. For example, interest in planning demonstrated by the space research community has inspired work in observation scheduling, planetary rover ex ploration and spacecraft control domains. Other temporal and resource-intensive domains including logistics planning, plant control and manufacturing have also helped to focus the community on the modelling and reasoning issues that must be confronted to make planning technology meet the challenges of application. The International Planning Competitions have acted as an important motivating force behind the progress that has been made in planning since 1998. The third competition (held in 2002) set the planning community the challenge of handling time and numeric resources. This necessitated the development of a modelling language capable of expressing temporal and numeric properties of planning domains. In this paper we describe the language, PDDL2.1, that was used in the competition. We describe the syntax of the language, its formal semantics and the validation of concurrent plans. We observe that PDDL2.1 has considerable modelling power --- exceeding the capabilities of current planning technology --- and presents a number of important challenges to the research community

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques

Simple Algorithm for Simple Timed Games

version 1.1We propose a subclass of timed game automata (TGA), called Task TGA, representing networks of communicating tasks where the system can choose when to start the task and the environment can choose the duration of the task. We search to solve finite-horizon reachability games on Task TGA by building strategies in the form of Simple Temporal Networks with Uncertainty (STNU). Such strategies have the advantage of being very succinct due to the partial order reduction of independent tasks. We show that the existence of such strategies is an NP-complete problem. A practical consequence of this result is a fully forward algorithm for building STNU strategies. Potential applications of this work are planning and scheduling under temporal uncertainty

A Multivariate Complexity Analysis of Qualitative Reasoning Problems

Qualitative reasoning is an important subfield of artificial intelligence where one describes relationships with qualitative, rather than numerical, relations. Many such reasoning tasks, e.g., Allen's interval algebra, can be solved in $2^{O(n \cdot \log n)}$ time, but single-exponential running times $2^{O(n)}$ are currently far out of reach. In this paper we consider single-exponential algorithms via a multivariate analysis consisting of a fine-grained parameter $n$ (e.g., the number of variables) and a coarse-grained parameter $k$ expected to be relatively small. We introduce the classes FPE and XE of problems solvable in $f(k) \cdot 2^{O(n)}$, respectively $f(k)^n$, time, and prove several fundamental properties of these classes. We proceed by studying temporal reasoning problems and (1) show that the Partially Ordered Time problem of effective width $k$ is solvable in $16^{kn}$ time and is thus included in XE, and (2) that the network consistency problem for Allen's interval algebra with no interval overlapping with more than $k$ others is solvable in $(2nk)^{2k} \cdot 2^{n}$ time and is included in FPE. Our multivariate approach is in no way limited to these to specific problems and may be a generally useful approach for obtaining single-exponential algorithms

Philosophy & The Discourse of Economics

'Samuelsonianism' can be used to refer to what is commonly called the neoclassical or mainstream approach to economics. In this paper I argue that it is this approach that is hindered by a rather contracted methodology, one which over-privileges the language of quantification. However, (to the benefit of economists) I argue that this methodology is itself resultant of a broader intellectual movement – what is called modernism. If we look carefully at the history of economics, much of the stringency that plagues the neoclassical approach can be traced to logical-positivism and the scientism of early ‘analytic’ philosophy. Thus, by considering the role that modernism played in philosophy and mapping its impact on economics, I show how this discourse, the hyper-quantified rhetoric of Samuelsonianism, is a relic of outmoded positivism. Consequently, economics could self-improve by seeking heterogeneity in its discourse and broadening its scope of analysis. While this paper is not an exercise in conceptual analysis per se, it does take language and rhetoric as both its point of departure and primary concern

Taming Numbers and Durations in the Model Checking Integrated Planning System

The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiveness in the benchmark problems and to achieve a high level of performance. The extensions include critical path analysis of sequentially generated plans to generate corresponding optimal parallel plans. The linear time algorithm to compute the parallel plan bypasses known NP hardness results for partial ordering by scheduling plans with respect to the set of actions and the imposed precedence relations. The efficiency of this algorithm also allows us to improve the exploration guidance: for each encountered planning state the corresponding approximate sequential plan is scheduled. One major strength of MIPS is its static analysis phase that grounds and simplifies parameterized predicates, functions and operators, that infers knowledge to minimize the state description length, and that detects domain object symmetries. The latter aspect is analyzed in detail. MIPS has been developed to serve as a complete and optimal state space planner, with admissible estimates, exploration engines and branching cuts. In the competition version, however, certain performance compromises had to be made, including floating point arithmetic, weighted heuristic search exploration according to an inadmissible estimate and parameterized optimization