2,597 research outputs found
Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies
Patriksson (2008) provided a then up-to-date survey on the
continuous,separable, differentiable and convex resource allocation problem
with a single resource constraint. Since the publication of that paper the
interest in the problem has grown: several new applications have arisen where
the problem at hand constitutes a subproblem, and several new algorithms have
been developed for its efficient solution. This paper therefore serves three
purposes. First, it provides an up-to-date extension of the survey of the
literature of the field, complementing the survey in Patriksson (2008) with
more then 20 books and articles. Second, it contributes improvements of some of
these algorithms, in particular with an improvement of the pegging (that is,
variable fixing) process in the relaxation algorithm, and an improved means to
evaluate subsolutions. Third, it numerically evaluates several relaxation
(primal) and breakpoint (dual) algorithms, incorporating a variety of pegging
strategies, as well as a quasi-Newton method. Our conclusion is that our
modification of the relaxation algorithm performs the best. At least for
problem sizes up to 30 million variables the practical time complexity for the
breakpoint and relaxation algorithms is linear
Top-k Multiclass SVM
Class ambiguity is typical in image classification problems with a large
number of classes. When classes are difficult to discriminate, it makes sense
to allow k guesses and evaluate classifiers based on the top-k error instead of
the standard zero-one loss. We propose top-k multiclass SVM as a direct method
to optimize for top-k performance. Our generalization of the well-known
multiclass SVM is based on a tight convex upper bound of the top-k error. We
propose a fast optimization scheme based on an efficient projection onto the
top-k simplex, which is of its own interest. Experiments on five datasets show
consistent improvements in top-k accuracy compared to various baselines.Comment: NIPS 201
MaxHedge: Maximising a Maximum Online
We introduce a new online learning framework where, at each trial, the
learner is required to select a subset of actions from a given known action
set. Each action is associated with an energy value, a reward and a cost. The
sum of the energies of the actions selected cannot exceed a given energy
budget. The goal is to maximise the cumulative profit, where the profit
obtained on a single trial is defined as the difference between the maximum
reward among the selected actions and the sum of their costs. Action energy
values and the budget are known and fixed. All rewards and costs associated
with each action change over time and are revealed at each trial only after the
learner's selection of actions. Our framework encompasses several online
learning problems where the environment changes over time; and the solution
trades-off between minimising the costs and maximising the maximum reward of
the selected subset of actions, while being constrained to an action energy
budget. The algorithm that we propose is efficient and general in that it may
be specialised to multiple natural online combinatorial problems.Comment: Published in AISTATS 201
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