Backdoors to planning

Backdoors measure the distance to tractable fragments and have become an important tool to find fixed-parameter tractable (fpt) algorithms for hard problems in AI and beyond. Despite their success, backdoors have not been used for planning, a central problem in AI that has a high computational complexity. In this work, we introduce two notions of backdoors building upon the causal graph. We analyze the complexity of finding a small backdoor (detection) and using the backdoor to solve the problem (evaluation) in the light of planning with (un)bounded plan length/domain of the variables. For each setting we present either an fpt-result or rule out the existence thereof by showing parameterized intractability. For several interesting cases we achieve the most desirable outcome: detection and evaluation are fpt. In addition, we explore the power of polynomial preprocessing for all fpt-results, i.e., we investigate whether polynomial kernels exist. We show that for the detection problems, polynomial kernels exist whereas we rule out the existence of polynomial kernels for the evaluation problems

Tractability in Constraint Satisfaction Problems: A Survey

International audienceEven though the Constraint Satisfaction Problem (CSP) is NP-complete, many tractable classes of CSP instances have been identified. After discussing different forms and uses of tractability, we describe some landmark tractable classes and survey recent theoretical results. Although we concentrate on the classical CSP, we also cover its important extensions to infinite domains and optimisation, as well as #CSP and QCSP

The Complexity of Planning Problems With Simple Causal Graphs

We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state variables and acyclic causal graphs. This implies that plan generation may be tractable even when a planning problem has an exponentially long minimal solution. We also prove that the problem of plan existence for planning problems with multi-valued variables and chain causal graphs is NP-hard. Finally, we show that plan existence for planning problems with binary state variables and polytree causal graphs is NP-complete

Doctor of Philosophy

dissertationTemporal reasoning denotes the modeling of causal relationships between different variables across different instances of time, and the prediction of future events or the explanation of past events. Temporal reasoning helps in modeling and understanding interactions between human pathophysiological processes, and in predicting future outcomes such as response to treatment or complications. Dynamic Bayesian Networks (DBN) support modeling changes in patients' condition over time due to both diseases and treatments, using probabilistic relationships between different clinical variables, both within and across different points in time. We describe temporal reasoning and representation in general and DBN in particular, with special attention to DBN parameter learning and inference. We also describe temporal data preparation (aggregation, consolidation, and abstraction) techniques that are applicable to medical data that were used in our research. We describe and evaluate various data discretization methods that are applicable to medical data. Projeny, an opensource probabilistic temporal reasoning toolkit developed as part of this research, is also described. We apply these methods, techniques, and algorithms to two disease processes modeled as Dynamic Bayesian Networks. The first test case is hyperglycemia due to severe illness in patients treated in the Intensive Care Unit (ICU). We model the patients' serum glucose and insulin drip rates using Dynamic Bayesian Networks, and recommend insulin drip rates to maintain the patients' serum glucose within a normal range. The model's safety and efficacy are proven by comparing it to the current gold standard. The second test case is the early prediction of sepsis in the emergency department. Sepsis is an acute life threatening condition that requires timely diagnosis and treatment. We present various DBN models and data preparation techniques that detect sepsis with very high accuracy within two hours after the patients' admission to the emergency department. We also discuss factors affecting the computational tractability of the models and appropriate optimization techniques. In this dissertation, we present a guide to temporal reasoning, evaluation of various data preparation, discretization, learning and inference methods, proofs using two test cases using real clinical data, an open-source toolkit, and recommend methods and techniques for temporal reasoning in medicine

Metareasoning about propagators for constraint satisfaction

Given the breadth of constraint satisfaction problems (CSPs) and the wide variety of CSP solvers, it is often very difficult to determine a priori which solving method is best suited to a problem. This work explores the use of machine learning to predict which solving method will be most effective for a given problem. We use four different problem sets to determine the CSP attributes that can be used to determine which solving method should be applied. After choosing an appropriate set of attributes, we determine how well j48 decision trees can predict which solving method to apply. Furthermore, we take a cost sensitive approach such that problem instances where there is a great difference in runtime between algorithms are emphasized. We also attempt to use information gained on one class of problems to inform decisions about a second class of problems. Finally, we show that the additional costs of deciding which method to apply are outweighed by the time savings compared to applying the same solving method to all problem instances

Universal Memory Architectures for Autonomous Machines

We propose a self-organizing memory architecture (UMA) for perceptual experience provably capable of supporting autonomous learning and goal-directed problem solving in the absence of any prior information about the agent’s environment. The architecture is simple enough to ensure (1) a quadratic bound (in the number of available sensors) on space requirements, and (2) a quadratic bound on the time-complexity of the update-execute cycle. At the same time, it is sufficiently complex to provide the agent with an internal representation which is (3) minimal among all representations which account for every sensory equivalence class consistent with the agent’s belief state; (4) capable, in principle, of recovering a topological model of the problem space; and (5) learnable with arbitrary precision through a random application of the available actions. These provable properties — both the trainability and the operational efficacy of an effectively trained memory structure — exploit a duality between weak poc sets — a symbolic (discrete) representation of subset nesting relations — and non-positively curved cubical complexes, whose rich convexity theory underlies the planning cycle of the proposed architecture