27,023 research outputs found
The Early Restart Algorithm
Consider an algorithm whose time to convergence is unknown (because of some random element in the algorithm, such as a random initial weight choice for neural network training). Consider the following strategy. Run the algorithm for a specific time T. If it has not converged by time T, cut the run short and rerun it from the start (repeat the same strategy for every run). This so-called restart mechanism has been proposed by Fahlman (1988) in the context of backpropagation training. It is advantageous in problems that are prone to local minima or when there is a large variability in convergence time from run to run, and may lead to a speed-up in such cases. In this article, we analyze theoretically the restart mechanism, and obtain conditions on the probability density of the convergence time for which restart will improve the expected convergence time. We also derive the optimal restart time. We apply the derived formulas to several cases, including steepest-descent algorithms
Variable Annealing Length and Parallelism in Simulated Annealing
In this paper, we propose: (a) a restart schedule for an adaptive simulated
annealer, and (b) parallel simulated annealing, with an adaptive and
parameter-free annealing schedule. The foundation of our approach is the
Modified Lam annealing schedule, which adaptively controls the temperature
parameter to track a theoretically ideal rate of acceptance of neighboring
states. A sequential implementation of Modified Lam simulated annealing is
almost parameter-free. However, it requires prior knowledge of the annealing
length. We eliminate this parameter using restarts, with an exponentially
increasing schedule of annealing lengths. We then extend this restart schedule
to parallel implementation, executing several Modified Lam simulated annealers
in parallel, with varying initial annealing lengths, and our proposed parallel
annealing length schedule. To validate our approach, we conduct experiments on
an NP-Hard scheduling problem with sequence-dependent setup constraints. We
compare our approach to fixed length restarts, both sequentially and in
parallel. Our results show that our approach can achieve substantial
performance gains, throughout the course of the run, demonstrating our approach
to be an effective anytime algorithm.Comment: Tenth International Symposium on Combinatorial Search, pages 2-10.
June 201
Speculative Concurrency Control for Real-Time Databases
In this paper, we propose a new class of Concurrency Control Algorithms that is especially suited for real-time database applications. Our approach relies on the use of (potentially) redundant computations to ensure that serializable schedules are found and executed as early as possible, thus, increasing the chances of a timely commitment of transactions with strict timing constraints. Due to its nature, we term our concurrency control algorithms Speculative. The aforementioned description encompasses many algorithms that we call collectively Speculative Concurrency Control (SCC) algorithms. SCC algorithms combine the advantages of both Pessimistic and Optimistic Concurrency Control (PCC and OCC) algorithms, while avoiding their disadvantages. On the one hand, SCC resembles PCC in that conflicts are detected as early as possible, thus making alternative schedules available in a timely fashion in case they are needed. On the other hand, SCC resembles OCC in that it allows conflicting transactions to proceed concurrently, thus avoiding unnecessary delays that may jeopardize their timely commitment
TPA: Fast, Scalable, and Accurate Method for Approximate Random Walk with Restart on Billion Scale Graphs
Given a large graph, how can we determine similarity between nodes in a fast
and accurate way? Random walk with restart (RWR) is a popular measure for this
purpose and has been exploited in numerous data mining applications including
ranking, anomaly detection, link prediction, and community detection. However,
previous methods for computing exact RWR require prohibitive storage sizes and
computational costs, and alternative methods which avoid such costs by
computing approximate RWR have limited accuracy. In this paper, we propose TPA,
a fast, scalable, and highly accurate method for computing approximate RWR on
large graphs. TPA exploits two important properties in RWR: 1) nodes close to a
seed node are likely to be revisited in following steps due to block-wise
structure of many real-world graphs, and 2) RWR scores of nodes which reside
far from the seed node are proportional to their PageRank scores. Based on
these two properties, TPA divides approximate RWR problem into two subproblems
called neighbor approximation and stranger approximation. In the neighbor
approximation, TPA estimates RWR scores of nodes close to the seed based on
scores of few early steps from the seed. In the stranger approximation, TPA
estimates RWR scores for nodes far from the seed using their PageRank. The
stranger and neighbor approximations are conducted in the preprocessing phase
and the online phase, respectively. Through extensive experiments, we show that
TPA requires up to 3.5x less time with up to 40x less memory space than other
state-of-the-art methods for the preprocessing phase. In the online phase, TPA
computes approximate RWR up to 30x faster than existing methods while
maintaining high accuracy.Comment: 12pages, 10 figure
Squeaky Wheel Optimization
We describe a general approach to optimization which we term `Squeaky Wheel'
Optimization (SWO). In SWO, a greedy algorithm is used to construct a solution
which is then analyzed to find the trouble spots, i.e., those elements, that,
if improved, are likely to improve the objective function score. The results of
the analysis are used to generate new priorities that determine the order in
which the greedy algorithm constructs the next solution. This
Construct/Analyze/Prioritize cycle continues until some limit is reached, or an
acceptable solution is found. SWO can be viewed as operating on two search
spaces: solutions and prioritizations. Successive solutions are only indirectly
related, via the re-prioritization that results from analyzing the prior
solution. Similarly, successive prioritizations are generated by constructing
and analyzing solutions. This `coupled search' has some interesting properties,
which we discuss. We report encouraging experimental results on two domains,
scheduling problems that arise in fiber-optic cable manufacturing, and graph
coloring problems. The fact that these domains are very different supports our
claim that SWO is a general technique for optimization
- β¦