14,499 research outputs found
On Decidable Growth-Rate Properties of Imperative Programs
In 2008, Ben-Amram, Jones and Kristiansen showed that for a simple "core"
programming language - an imperative language with bounded loops, and
arithmetics limited to addition and multiplication - it was possible to decide
precisely whether a program had certain growth-rate properties, namely
polynomial (or linear) bounds on computed values, or on the running time.
This work emphasized the role of the core language in mitigating the
notorious undecidability of program properties, so that one deals with
decidable problems.
A natural and intriguing problem was whether more elements can be added to
the core language, improving its utility, while keeping the growth-rate
properties decidable. In particular, the method presented could not handle a
command that resets a variable to zero. This paper shows how to handle resets.
The analysis is given in a logical style (proof rules), and its complexity is
shown to be PSPACE-complete (in contrast, without resets, the problem was
PTIME). The analysis algorithm evolved from the previous solution in an
interesting way: focus was shifted from proving a bound to disproving it, and
the algorithm works top-down rather than bottom-up
Graphical Models for Optimal Power Flow
Optimal power flow (OPF) is the central optimization problem in electric
power grids. Although solved routinely in the course of power grid operations,
it is known to be strongly NP-hard in general, and weakly NP-hard over tree
networks. In this paper, we formulate the optimal power flow problem over tree
networks as an inference problem over a tree-structured graphical model where
the nodal variables are low-dimensional vectors. We adapt the standard dynamic
programming algorithm for inference over a tree-structured graphical model to
the OPF problem. Combining this with an interval discretization of the nodal
variables, we develop an approximation algorithm for the OPF problem. Further,
we use techniques from constraint programming (CP) to perform interval
computations and adaptive bound propagation to obtain practically efficient
algorithms. Compared to previous algorithms that solve OPF with optimality
guarantees using convex relaxations, our approach is able to work for arbitrary
distribution networks and handle mixed-integer optimization problems. Further,
it can be implemented in a distributed message-passing fashion that is scalable
and is suitable for "smart grid" applications like control of distributed
energy resources. We evaluate our technique numerically on several benchmark
networks and show that practical OPF problems can be solved effectively using
this approach.Comment: To appear in Proceedings of the 22nd International Conference on
Principles and Practice of Constraint Programming (CP 2016
Variational Bayesian inference for linear and logistic regression
The article describe the model, derivation, and implementation of variational
Bayesian inference for linear and logistic regression, both with and without
automatic relevance determination. It has the dual function of acting as a
tutorial for the derivation of variational Bayesian inference for simple
models, as well as documenting, and providing brief examples for the
MATLAB/Octave functions that implement this inference. These functions are
freely available online.Comment: 28 pages, 6 figure
Hierarchical Decomposition of Nonlinear Dynamics and Control for System Identification and Policy Distillation
The control of nonlinear dynamical systems remains a major challenge for
autonomous agents. Current trends in reinforcement learning (RL) focus on
complex representations of dynamics and policies, which have yielded impressive
results in solving a variety of hard control tasks. However, this new
sophistication and extremely over-parameterized models have come with the cost
of an overall reduction in our ability to interpret the resulting policies. In
this paper, we take inspiration from the control community and apply the
principles of hybrid switching systems in order to break down complex dynamics
into simpler components. We exploit the rich representational power of
probabilistic graphical models and derive an expectation-maximization (EM)
algorithm for learning a sequence model to capture the temporal structure of
the data and automatically decompose nonlinear dynamics into stochastic
switching linear dynamical systems. Moreover, we show how this framework of
switching models enables extracting hierarchies of Markovian and
auto-regressive locally linear controllers from nonlinear experts in an
imitation learning scenario.Comment: 2nd Annual Conference on Learning for Dynamics and Contro
Invariant Generation for Multi-Path Loops with Polynomial Assignments
Program analysis requires the generation of program properties expressing
conditions to hold at intermediate program locations. When it comes to programs
with loops, these properties are typically expressed as loop invariants. In
this paper we study a class of multi-path program loops with numeric variables,
in particular nested loops with conditionals, where assignments to program
variables are polynomial expressions over program variables. We call this class
of loops extended P-solvable and introduce an algorithm for generating all
polynomial invariants of such loops. By an iterative procedure employing
Gr\"obner basis computation, our approach computes the polynomial ideal of the
polynomial invariants of each program path and combines these ideals
sequentially until a fixed point is reached. This fixed point represents the
polynomial ideal of all polynomial invariants of the given extended P-solvable
loop. We prove termination of our method and show that the maximal number of
iterations for reaching the fixed point depends linearly on the number of
program variables and the number of inner loops. In particular, for a loop with
m program variables and r conditional branches we prove an upper bound of m*r
iterations. We implemented our approach in the Aligator software package.
Furthermore, we evaluated it on 18 programs with polynomial arithmetic and
compared it to existing methods in invariant generation. The results show the
efficiency of our approach
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