94,853 research outputs found
OneMax in Black-Box Models with Several Restrictions
Black-box complexity studies lower bounds for the efficiency of
general-purpose black-box optimization algorithms such as evolutionary
algorithms and other search heuristics. Different models exist, each one being
designed to analyze a different aspect of typical heuristics such as the memory
size or the variation operators in use. While most of the previous works focus
on one particular such aspect, we consider in this work how the combination of
several algorithmic restrictions influence the black-box complexity. Our
testbed are so-called OneMax functions, a classical set of test functions that
is intimately related to classic coin-weighing problems and to the board game
Mastermind.
We analyze in particular the combined memory-restricted ranking-based
black-box complexity of OneMax for different memory sizes. While its isolated
memory-restricted as well as its ranking-based black-box complexity for bit
strings of length is only of order , the combined model does not
allow for algorithms being faster than linear in , as can be seen by
standard information-theoretic considerations. We show that this linear bound
is indeed asymptotically tight. Similar results are obtained for other memory-
and offspring-sizes. Our results also apply to the (Monte Carlo) complexity of
OneMax in the recently introduced elitist model, in which only the best-so-far
solution can be kept in the memory. Finally, we also provide improved lower
bounds for the complexity of OneMax in the regarded models.
Our result enlivens the quest for natural evolutionary algorithms optimizing
OneMax in iterations.Comment: This is the full version of a paper accepted to GECCO 201
Optimizing a Certified Proof Checker for a Large-Scale Computer-Generated Proof
In recent work, we formalized the theory of optimal-size sorting networks
with the goal of extracting a verified checker for the large-scale
computer-generated proof that 25 comparisons are optimal when sorting 9 inputs,
which required more than a decade of CPU time and produced 27 GB of proof
witnesses. The checker uses an untrusted oracle based on these witnesses and is
able to verify the smaller case of 8 inputs within a couple of days, but it did
not scale to the full proof for 9 inputs. In this paper, we describe several
non-trivial optimizations of the algorithm in the checker, obtained by
appropriately changing the formalization and capitalizing on the symbiosis with
an adequate implementation of the oracle. We provide experimental evidence of
orders of magnitude improvements to both runtime and memory footprint for 8
inputs, and actually manage to check the full proof for 9 inputs.Comment: IMADA-preprint-c
Optimising Trade-offs Among Stakeholders in Ad Auctions
We examine trade-offs among stakeholders in ad auctions. Our metrics are the
revenue for the utility of the auctioneer, the number of clicks for the utility
of the users and the welfare for the utility of the advertisers. We show how to
optimize linear combinations of the stakeholder utilities, showing that these
can be tackled through a GSP auction with a per-click reserve price. We then
examine constrained optimization of stakeholder utilities.
We use simulations and analysis of real-world sponsored search auction data
to demonstrate the feasible trade-offs, examining the effect of changing the
allowed number of ads on the utilities of the stakeholders. We investigate both
short term effects, when the players do not have the time to modify their
behavior, and long term equilibrium conditions.
Finally, we examine a combinatorially richer constrained optimization
problem, where there are several possible allowed configurations (templates) of
ad formats. This model captures richer ad formats, which allow using the
available screen real estate in various ways. We show that two natural
generalizations of the GSP auction rules to this domain are poorly behaved,
resulting in not having a symmetric Nash equilibrium or having one with poor
welfare. We also provide positive results for restricted cases.Comment: 18 pages, 10 figures, ACM Conference on Economics and Computation
201
Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reserve
Second-price auctions with reserve play a critical role for modern search
engine and popular online sites since the revenue of these companies often
directly de- pends on the outcome of such auctions. The choice of the reserve
price is the main mechanism through which the auction revenue can be influenced
in these electronic markets. We cast the problem of selecting the reserve price
to optimize revenue as a learning problem and present a full theoretical
analysis dealing with the complex properties of the corresponding loss
function. We further give novel algorithms for solving this problem and report
the results of several experiments in both synthetic and real data
demonstrating their effectiveness.Comment: Accepted at ICML 201
Barrier Frank-Wolfe for Marginal Inference
We introduce a globally-convergent algorithm for optimizing the
tree-reweighted (TRW) variational objective over the marginal polytope. The
algorithm is based on the conditional gradient method (Frank-Wolfe) and moves
pseudomarginals within the marginal polytope through repeated maximum a
posteriori (MAP) calls. This modular structure enables us to leverage black-box
MAP solvers (both exact and approximate) for variational inference, and obtains
more accurate results than tree-reweighted algorithms that optimize over the
local consistency relaxation. Theoretically, we bound the sub-optimality for
the proposed algorithm despite the TRW objective having unbounded gradients at
the boundary of the marginal polytope. Empirically, we demonstrate the
increased quality of results found by tightening the relaxation over the
marginal polytope as well as the spanning tree polytope on synthetic and
real-world instances.Comment: 25 pages, 12 figures, To appear in Neural Information Processing
Systems (NIPS) 2015, Corrected reference and cleaned up bibliograph
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