1,002 research outputs found
Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems
We propose a simple, powerful, and flexible machine learning framework for
(i) reducing the search space of computationally difficult enumeration variants
of subset problems and (ii) augmenting existing state-of-the-art solvers with
informative cues arising from the input distribution. We instantiate our
framework for the problem of listing all maximum cliques in a graph, a central
problem in network analysis, data mining, and computational biology. We
demonstrate the practicality of our approach on real-world networks with
millions of vertices and edges by not only retaining all optimal solutions, but
also aggressively pruning the input instance size resulting in several fold
speedups of state-of-the-art algorithms. Finally, we explore the limits of
scalability and robustness of our proposed framework, suggesting that
supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201
Safety-Aware Apprenticeship Learning
Apprenticeship learning (AL) is a kind of Learning from Demonstration
techniques where the reward function of a Markov Decision Process (MDP) is
unknown to the learning agent and the agent has to derive a good policy by
observing an expert's demonstrations. In this paper, we study the problem of
how to make AL algorithms inherently safe while still meeting its learning
objective. We consider a setting where the unknown reward function is assumed
to be a linear combination of a set of state features, and the safety property
is specified in Probabilistic Computation Tree Logic (PCTL). By embedding
probabilistic model checking inside AL, we propose a novel
counterexample-guided approach that can ensure safety while retaining
performance of the learnt policy. We demonstrate the effectiveness of our
approach on several challenging AL scenarios where safety is essential.Comment: Accepted by International Conference on Computer Aided Verification
(CAV) 201
Probabilistic satisfiability
AbstractWe study the following computational problem proposed by Nils Nilsson: Several clauses (disjunctions of literals) are given, and for each clause the probability that the clause is true is specified. We are asked whether these probabilities are consistent. They are if there is a probability distribution on the truth assignments such that the probability of each clause is the measure of its satisfying set of assignments. Since this problem is a generalization of the satisfiability problem for propositional calculus it is immediately NP-hard. We show that it is NP-complete even when there are at most two literals per clause (a case which is polynomial-time solvable in the non-probabilistic case). We use arguments from linear programming and graph theory to derive polynomial-time algorithms for some interesting special cases
Transfer Function Synthesis without Quantifier Elimination
Traditionally, transfer functions have been designed manually for each
operation in a program, instruction by instruction. In such a setting, a
transfer function describes the semantics of a single instruction, detailing
how a given abstract input state is mapped to an abstract output state. The net
effect of a sequence of instructions, a basic block, can then be calculated by
composing the transfer functions of the constituent instructions. However,
precision can be improved by applying a single transfer function that captures
the semantics of the block as a whole. Since blocks are program-dependent, this
approach necessitates automation. There has thus been growing interest in
computing transfer functions automatically, most notably using techniques based
on quantifier elimination. Although conceptually elegant, quantifier
elimination inevitably induces a computational bottleneck, which limits the
applicability of these methods to small blocks. This paper contributes a method
for calculating transfer functions that finesses quantifier elimination
altogether, and can thus be seen as a response to this problem. The
practicality of the method is demonstrated by generating transfer functions for
input and output states that are described by linear template constraints,
which include intervals and octagons.Comment: 37 pages, extended version of ESOP 2011 pape
Exact and Efficient Simulation of Concordant Computation
Concordant computation is a circuit-based model of quantum computation for
mixed states, that assumes that all correlations within the register are
discord-free (i.e. the correlations are essentially classical) at every step of
the computation. The question of whether concordant computation always admits
efficient simulation by a classical computer was first considered by B. Eastin
in quant-ph/1006.4402v1, where an answer in the affirmative was given for
circuits consisting only of one- and two-qubit gates. Building on this work, we
develop the theory of classical simulation of concordant computation. We
present a new framework for understanding such computations, argue that a
larger class of concordant computations admit efficient simulation, and provide
alternative proofs for the main results of quant-ph/1006.4402v1 with an
emphasis on the exactness of simulation which is crucial for this model. We
include detailed analysis of the arithmetic complexity for solving equations in
the simulation, as well as extensions to larger gates and qudits. We explore
the limitations of our approach, and discuss the challenges faced in developing
efficient classical simulation algorithms for all concordant computations.Comment: 16 page
Safety-aware apprenticeship learning
It is well acknowledged in the AI community that finding a good reward function for reinforcement learning is extremely challenging. Apprenticeship learning (AL) is a class of “learning from demonstration” techniques where the reward function of a Markov Decision Process (MDP) is unknown to the learning agent and the agent uses inverse reinforcement learning (IRL) methods to recover expert policy from a set of expert demonstrations. However, as the agent learns exclusively from observations, given a constraint on the probability of the agent running into unwanted situations, there is no verification, nor guarantee, for the learnt policy on the satisfaction of the restriction. In this dissertation, we study the problem of how to guide AL to learn a policy that is inherently safe while still meeting its learning objective. By combining formal methods with imitation learning, a Counterexample-Guided Apprenticeship Learning algorithm is proposed. We consider a setting where the unknown reward function is assumed to be a linear combination of a set of state features, and the safety property is specified in Probabilistic Computation Tree Logic (PCTL). By embedding probabilistic model checking inside AL, we propose a novel counterexample-guided approach that can ensure both safety and performance of the learnt policy. This algorithm guarantees that given some formal safety specification defined by probabilistic temporal logic, the learnt policy shall satisfy this specification. We demonstrate the effectiveness of our approach on several challenging AL scenarios where safety is essential
Anytime system level verification via parallel random exhaustive hardware in the loop simulation
System level verification of cyber-physical systems has the goal of verifying that the whole (i.e., software + hardware) system meets the given specifications. Model checkers for hybrid systems cannot handle system level verification of actual systems. Thus, Hardware In the Loop Simulation (HILS) is currently the main workhorse for system level verification. By using model checking driven exhaustive HILS, System Level Formal Verification (SLFV) can be effectively carried out for actual systems.
We present a parallel random exhaustive HILS based model checker for hybrid systems that, by simulating all operational scenarios exactly once in a uniform random order, is able to provide, at any time during the verification process, an upper bound to the probability that the System Under Verification exhibits an error in a yet-to-be-simulated scenario (Omission Probability).
We show effectiveness of the proposed approach by presenting experimental results on SLFV of the Inverted Pendulum on a Cart and the Fuel Control System examples in the Simulink distribution. To the best of our knowledge, no previously published model checker can exhaustively verify hybrid systems of such a size and provide at any time an upper bound to the Omission Probability
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