6 research outputs found
Adaptivity and Optimality: A Universal Algorithm for Online Convex Optimization
In this paper, we study adaptive online convex optimization, and aim to
design a universal algorithm that achieves optimal regret bounds for multiple
common types of loss functions. Existing universal methods are limited in the
sense that they are optimal for only a subclass of loss functions. To address
this limitation, we propose a novel online method, namely Maler, which enjoys
the optimal , and regret bounds for
general convex, exponentially concave, and strongly convex functions
respectively. The essential idea is to run multiple types of learning
algorithms with different learning rates in parallel, and utilize a meta
algorithm to track the best one on the fly. Empirical results demonstrate the
effectiveness of our method.Comment: 12 pages, 2 figure
Adaptive Regret of Convex and Smooth Functions
We investigate online convex optimization in changing environments, and
choose the adaptive regret as the performance measure. The goal is to achieve a
small regret over every interval so that the comparator is allowed to change
over time. Different from previous works that only utilize the convexity
condition, this paper further exploits smoothness to improve the adaptive
regret. To this end, we develop novel adaptive algorithms for convex and smooth
functions, and establish problem-dependent regret bounds over any interval. Our
regret bounds are comparable to existing results in the worst case, and become
much tighter when the comparator has a small loss
Dynamic Local Regret for Non-convex Online Forecasting
We consider online forecasting problems for non-convex machine learning
models. Forecasting introduces several challenges such as (i) frequent updates
are necessary to deal with concept drift issues since the dynamics of the
environment change over time, and (ii) the state of the art models are
non-convex models. We address these challenges with a novel regret framework.
Standard regret measures commonly do not consider both dynamic environment and
non-convex models. We introduce a local regret for non-convex models in a
dynamic environment. We present an update rule incurring a cost, according to
our proposed local regret, which is sublinear in time T. Our update uses
time-smoothed gradients. Using a real-world dataset we show that our
time-smoothed approach yields several benefits when compared with
state-of-the-art competitors: results are more stable against new data;
training is more robust to hyperparameter selection; and our approach is more
computationally efficient than the alternatives.Comment: NeurIPS2019. arXiv admin note: substantial text overlap with
arXiv:1905.0885
Dual Adaptivity: A Universal Algorithm for Minimizing the Adaptive Regret of Convex Functions
To deal with changing environments, a new performance measure---adaptive
regret, defined as the maximum static regret over any interval, is proposed in
online learning. Under the setting of online convex optimization, several
algorithms have been successfully developed to minimize the adaptive regret.
However, existing algorithms lack universality in the sense that they can only
handle one type of convex functions and need apriori knowledge of parameters.
By contrast, there exist universal algorithms, such as MetaGrad, that attain
optimal static regret for multiple types of convex functions simultaneously.
Along this line of research, this paper presents the first universal algorithm
for minimizing the adaptive regret of convex functions. Specifically, we borrow
the idea of maintaining multiple learning rates in MetaGrad to handle the
uncertainty of functions, and utilize the technique of sleeping experts to
capture changing environments. In this way, our algorithm automatically adapts
to the property of functions (convex, exponentially concave, or strongly
convex), as well as the nature of environments (stationary or changing). As a
by product, it also allows the type of functions to switch between rounds
Bandit Convex Optimization in Non-stationary Environments
Bandit Convex Optimization (BCO) is a fundamental framework for modeling
sequential decision-making with partial information, where the only feedback
available to the player is the one-point or two-point function values. In this
paper, we investigate BCO in non-stationary environments and choose the
\emph{dynamic regret} as the performance measure, which is defined as the
difference between the cumulative loss incurred by the algorithm and that of
any feasible comparator sequence. Let be the time horizon and be the
path-length of the comparator sequence that reflects the non-stationarity of
environments. We propose a novel algorithm that achieves
and dynamic regret
respectively for the one-point and two-point feedback models. The latter result
is optimal, matching the lower bound established
in this paper. Notably, our algorithm is more adaptive to non-stationary
environments since it does not require prior knowledge of the path-length
ahead of time, which is generally unknown
DriftSurf: A Risk-competitive Learning Algorithm under Concept Drift
When learning from streaming data, a change in the data distribution, also
known as concept drift, can render a previously-learned model inaccurate and
require training a new model. We present an adaptive learning algorithm that
extends previous drift-detection-based methods by incorporating drift detection
into a broader stable-state/reactive-state process. The advantage of our
approach is that we can use aggressive drift detection in the stable state to
achieve a high detection rate, but mitigate the false positive rate of
standalone drift detection via a reactive state that reacts quickly to true
drifts while eliminating most false positives. The algorithm is generic in its
base learner and can be applied across a variety of supervised learning
problems. Our theoretical analysis shows that the risk of the algorithm is
competitive to an algorithm with oracle knowledge of when (abrupt) drifts
occur. Experiments on synthetic and real datasets with concept drifts confirm
our theoretical analysis.Comment: 32 pages, 12 figures. Submitted to NeurIPS 2020. Replaced to include
revision of Lemma 2 and additional experimental result