1,007 research outputs found
Online Learning for Changing Environments using Coin Betting
A key challenge in online learning is that classical algorithms can be slow
to adapt to changing environments. Recent studies have proposed "meta"
algorithms that convert any online learning algorithm to one that is adaptive
to changing environments, where the adaptivity is analyzed in a quantity called
the strongly-adaptive regret. This paper describes a new meta algorithm that
has a strongly-adaptive regret bound that is a factor of
better than other algorithms with the same time complexity, where is the
time horizon. We also extend our algorithm to achieve a first-order (i.e.,
dependent on the observed losses) strongly-adaptive regret bound for the first
time, to our knowledge. At its heart is a new parameter-free algorithm for the
learning with expert advice (LEA) problem in which experts sometimes do not
output advice for consecutive time steps (i.e., \emph{sleeping} experts). This
algorithm is derived by a reduction from optimal algorithms for the so-called
coin betting problem. Empirical results show that our algorithm outperforms
state-of-the-art methods in both learning with expert advice and metric
learning scenarios.Comment: submitted to a journal. arXiv admin note: substantial text overlap
with arXiv:1610.0457
Training Deep Networks without Learning Rates Through Coin Betting
Deep learning methods achieve state-of-the-art performance in many application scenarios. Yet, these methods require a significant amount of hyperparameters tuning in order to achieve the best results. In particular, tuning the learning rates in the stochastic optimization process is still one of the main bottlenecks. In this paper, we propose a new stochastic gradient descent procedure for deep networks that does not require any learning rate setting. Contrary to previous methods, we do not adapt the learning rates nor we make use of the assumed curvature of the objective function. Instead, we reduce the optimization process to a game of betting on a coin and propose a learning rate free optimal algorithm for this scenario. Theoretical convergence is proven for convex and quasi-convex functions and empirical evidence shows the advantage of our algorithm over popular stochastic gradient algorithms
A Modern Introduction to Online Learning
In this monograph, I introduce the basic concepts of Online Learning through
a modern view of Online Convex Optimization. Here, online learning refers to
the framework of regret minimization under worst-case assumptions. I present
first-order and second-order algorithms for online learning with convex losses,
in Euclidean and non-Euclidean settings. All the algorithms are clearly
presented as instantiation of Online Mirror Descent or
Follow-The-Regularized-Leader and their variants. Particular attention is given
to the issue of tuning the parameters of the algorithms and learning in
unbounded domains, through adaptive and parameter-free online learning
algorithms. Non-convex losses are dealt through convex surrogate losses and
through randomization. The bandit setting is also briefly discussed, touching
on the problem of adversarial and stochastic multi-armed bandits. These notes
do not require prior knowledge of convex analysis and all the required
mathematical tools are rigorously explained. Moreover, all the proofs have been
carefully chosen to be as simple and as short as possible.Comment: Fixed more typos, added more history bits, added local norms bounds
for OMD and FTR
Parameter-free locally differentially private stochastic subgradient descent
https://arxiv.org/pdf/1911.09564.pdfhttps://arxiv.org/pdf/1911.09564.pdfhttps://arxiv.org/pdf/1911.09564.pdfhttps://arxiv.org/pdf/1911.09564.pdfhttps://arxiv.org/pdf/1911.09564.pdfhttps://arxiv.org/pdf/1911.09564.pdfPublished versio
Better Parameter-free Stochastic Optimization with ODE Updates for Coin-Betting
Parameter-free stochastic gradient descent (PFSGD) algorithms do not require
setting learning rates while achieving optimal theoretical performance. In
practical applications, however, there remains an empirical gap between tuned
stochastic gradient descent (SGD) and PFSGD. In this paper, we close the
empirical gap with a new parameter-free algorithm based on continuous-time
Coin-Betting on truncated models. The new update is derived through the
solution of an Ordinary Differential Equation (ODE) and solved in a closed
form. We show empirically that this new parameter-free algorithm outperforms
algorithms with the "best default" learning rates and almost matches the
performance of finely tuned baselines without anything to tune
Parameter-Free Online Convex Optimization with Sub-Exponential Noise
We consider the problem of unconstrained online convex optimization (OCO)
with sub-exponential noise, a strictly more general problem than the standard
OCO. In this setting, the learner receives a subgradient of the loss functions
corrupted by sub-exponential noise and strives to achieve optimal regret
guarantee, without knowledge of the competitor norm, i.e., in a parameter-free
way. Recently, Cutkosky and Boahen (COLT 2017) proved that, given unbounded
subgradients, it is impossible to guarantee a sublinear regret due to an
exponential penalty. This paper shows that it is possible to go around the
lower bound by allowing the observed subgradients to be unbounded via
stochastic noise. However, the presence of unbounded noise in unconstrained OCO
is challenging; existing algorithms do not provide near-optimal regret bounds
or fail to have a guarantee. So, we design a novel parameter-free OCO algorithm
for Banach space, which we call BANCO, via a reduction to betting on noisy
coins. We show that BANCO achieves the optimal regret rate in our problem.
Finally, we show the application of our results to obtain a parameter-free
locally private stochastic subgradient descent algorithm, and the connection to
the law of iterated logarithms.Comment: v1: Accepted to COLT'19, v2: adjusted Theorem 3, w_t closed form
solution, and typo
CoinEM: Tuning-Free Particle-Based Variational Inference for Latent Variable Models
We introduce two new particle-based algorithms for learning latent variable
models via marginal maximum likelihood estimation, including one which is
entirely tuning-free. Our methods are based on the perspective of marginal
maximum likelihood estimation as an optimization problem: namely, as the
minimization of a free energy functional. One way to solve this problem is to
consider the discretization of a gradient flow associated with the free energy.
We study one such approach, which resembles an extension of the popular Stein
variational gradient descent algorithm. In particular, we establish a descent
lemma for this algorithm, which guarantees that the free energy decreases at
each iteration. This method, and any other obtained as the discretization of
the gradient flow, will necessarily depend on a learning rate which must be
carefully tuned by the practitioner in order to ensure convergence at a
suitable rate. With this in mind, we also propose another algorithm for
optimizing the free energy which is entirely learning rate free, based on coin
betting techniques from convex optimization. We validate the performance of our
algorithms across a broad range of numerical experiments, including several
high-dimensional settings. Our results are competitive with existing
particle-based methods, without the need for any hyperparameter tuning
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