207 research outputs found
Optimal No-regret Learning in Repeated First-price Auctions
We study online learning in repeated first-price auctions with censored
feedback, where a bidder, only observing the winning bid at the end of each
auction, learns to adaptively bid in order to maximize her cumulative payoff.
To achieve this goal, the bidder faces a challenging dilemma: if she wins the
bid--the only way to achieve positive payoffs--then she is not able to observe
the highest bid of the other bidders, which we assume is iid drawn from an
unknown distribution. This dilemma, despite being reminiscent of the
exploration-exploitation trade-off in contextual bandits, cannot directly be
addressed by the existing UCB or Thompson sampling algorithms in that
literature, mainly because contrary to the standard bandits setting, when a
positive reward is obtained here, nothing about the environment can be learned.
In this paper, by exploiting the structural properties of first-price
auctions, we develop the first learning algorithm that achieves
regret bound when the bidder's private values are
stochastically generated. We do so by providing an algorithm on a general class
of problems, which we call monotone group contextual bandits, where the same
regret bound is established under stochastically generated contexts. Further,
by a novel lower bound argument, we characterize an lower
bound for the case where the contexts are adversarially generated, thus
highlighting the impact of the contexts generation mechanism on the fundamental
learning limit. Despite this, we further exploit the structure of first-price
auctions and develop a learning algorithm that operates sample-efficiently (and
computationally efficiently) in the presence of adversarially generated private
values. We establish an regret bound for this algorithm,
hence providing a complete characterization of optimal learning guarantees for
this problem
Development of Hypoxia Trapping Enhanced BB2R-Targeted Radiopharmaceutics for Prostate Cancer
The Gastrin-Releasing Peptide Receptor (BB2r) has been investigated as a diagnostic and therapeutic target for prostate and other cancers due to the high expression level on neoplastic relative to normal tissues. A variety of BB2r-targeted agents have been developed utilizing the bombesin(BBN) peptide, which has shown nanomolar binding affinity to human BB2r. However, as with most of the low-molecular weight, receptor-targeted drugs, a major challenge to clinical translation of BB2r-targeted agents is the low retention at the tumor site due to intrinsically high diffusion and efflux rates. Our laboratory seeks to address this deficiency by developing synthetic approaches to selectively increase retention of BB2r-targeted agents in prostate cancer. Hypoxic regions commonly exist in prostate tumors and many other cancers due to a chaotic vascular architecture which impedes delivery of oxygen. In this dissertation, we explore the incorporation of nitroimidazoles, a hypoxia-selective prodrug which irreversibly binds to intracellular nucleophiles in hypoxic tissues, into the BB2r-targeted agent paradigm. We seek to determine if these agents can increase the long-term retention in the tumor and thereby increase efficacy and clinical potential of BB2r-targeted agents.
To that end, we have developed several generations of hypoxia trapping enhanced BBN analogs. Our first in vitro investigation of hypoxia-enhanced 111In-labeled BBN conjugates demonstrated significantly improved retention in hypoxic PC-3 human prostate cancer cells. However, it was determined that the proximity of the 2-nitroimidazole relative to the pharmacophore had a detrimental impact on BB2r binding affinity. To address the problem, our next generation of radioconjugates contained an extended linker to eliminate steric inhibition. The new design demonstrated substantially improved binding affinity and lower clearance rate of the 2-nitroimidazole containing radioconjugates under hypoxic conditions. In vivo biodistribution studies using a PC-3 xenograft mouse model revealed significant tumor retention enhancement. Further work is needed to clarify the mechanisms of cellular retention and to correlate the tumor hypoxia burden with the retention efficacy
Stochastic Nonsmooth Convex Optimization with Heavy-Tailed Noises
Recently, several studies consider the stochastic optimization problem but in
a heavy-tailed noise regime, i.e., the difference between the stochastic
gradient and the true gradient is assumed to have a finite -th moment (say
being upper bounded by for some ) where ,
which not only generalizes the traditional finite variance assumption ()
but also has been observed in practice for several different tasks. Under this
challenging assumption, lots of new progress has been made for either convex or
nonconvex problems, however, most of which only consider smooth objectives. In
contrast, people have not fully explored and well understood this problem when
functions are nonsmooth. This paper aims to fill this crucial gap by providing
a comprehensive analysis of stochastic nonsmooth convex optimization with
heavy-tailed noises. We revisit a simple clipping-based algorithm, whereas,
which is only proved to converge in expectation but under the additional strong
convexity assumption. Under appropriate choices of parameters, for both convex
and strongly convex functions, we not only establish the first high-probability
rates but also give refined in-expectation bounds compared with existing works.
Remarkably, all of our results are optimal (or nearly optimal up to logarithmic
factors) with respect to the time horizon even when is unknown in
advance. Additionally, we show how to make the algorithm parameter-free with
respect to , in other words, the algorithm can still guarantee
convergence without any prior knowledge of
Revisiting the Last-Iterate Convergence of Stochastic Gradient Methods
In the past several years, the last-iterate convergence of the Stochastic
Gradient Descent (SGD) algorithm has triggered people's interest due to its
good performance in practice but lack of theoretical understanding. For
Lipschitz convex functions, different works have established the optimal
or
high-probability convergence rates for the final iterate, where is the time
horizon and is the failure probability. However, to prove these
bounds, all the existing works are either limited to compact domains or require
almost surely bounded noises. It is natural to ask whether the last iterate of
SGD can still guarantee the optimal convergence rate but without these two
restrictive assumptions. Besides this important question, there are still lots
of theoretical problems lacking an answer. For example, compared with the
last-iterate convergence of SGD for non-smooth problems, only few results for
smooth optimization have yet been developed. Additionally, the existing results
are all limited to a non-composite objective and the standard Euclidean norm.
It still remains unclear whether the last-iterate convergence can be provably
extended to wider composite optimization and non-Euclidean norms. In this work,
to address the issues mentioned above, we revisit the last-iterate convergence
of stochastic gradient methods and provide the first unified way to prove the
convergence rates both in expectation and in high probability to accommodate
general domains, composite objectives, non-Euclidean norms, Lipschitz
conditions, smoothness, and (strong) convexity simultaneously. Additionally, we
extend our analysis to obtain the last-iterate convergence under heavy-tailed
noises.Comment: The preliminary version has been accepted at ICLR 2024. This extended
version was finished in November 2023 and revised in March 2024 with fixed
typo
On the Last-Iterate Convergence of Shuffling Gradient Methods
Shuffling gradient methods are widely used in modern machine learning tasks
and include three popular implementations: Random Reshuffle (RR), Shuffle Once
(SO), and Incremental Gradient (IG). Compared to the empirical success, the
theoretical guarantee of shuffling gradient methods was not well-understood for
a long time. Until recently, the convergence rates had just been established
for the average iterate for convex functions and the last iterate for strongly
convex problems (using squared distance as the metric). However, when using the
function value gap as the convergence criterion, existing theories cannot
interpret the good performance of the last iterate in different settings (e.g.,
constrained optimization). To bridge this gap between practice and theory, we
prove the first last-iterate convergence rates for shuffling gradient methods
with respect to the objective value even without strong convexity. Our new
results either (nearly) match the existing last-iterate lower bounds or are as
fast as the previous best upper bounds for the average iterate.Comment: ICML 202
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