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Operationalizing Stein's Method for Online Linear Optimization: CLT-Based Optimal Tradeoffs

arXiv.org Machine Learning

Adversarial online linear optimization (OLO) is essentially about making performance tradeoffs with respect to the unknown difficulty of the adversary. In the setting of one-dimensional fixed-time OLO on a bounded domain, it has been observed since Cover (1966) that achievable tradeoffs are governed by probabilistic inequalities, and these descriptive results can be converted into algorithms via dynamic programming, which, however, is not computationally efficient. We address this limitation by showing that Stein's method, a classical framework underlying the proofs of probabilistic limit theorems, can be operationalized as computationally efficient OLO algorithms. The associated regret and total loss upper bounds are "additively sharp", meaning that they surpass the conventional big-O optimality and match normal-approximation-based lower bounds by additive lower order terms. Our construction is inspired by the remarkably clean proof of a Wasserstein martingale central limit theorem (CLT) due to Rรถllin (2018). Several concrete benefits can be obtained from this general technique. First, with the same computational complexity, the proposed algorithm improves upon the total loss upper bounds of online gradient descent (OGD) and multiplicative weight update (MWU). Second, our algorithm can realize a continuum of optimal two-point tradeoffs between the total loss and the maximum regret over comparators, improving upon prior works in parameter-free online learning. Third, by allowing the adversary to randomize on an unbounded support, we achieve sharp in-expectation performance guarantees for OLO with noisy feedback.



Have scientists discovered a new colour called 'olo'?

Al Jazeera

A team of scientists claims to have discovered a new colour that humans cannot see without the help of technology. The researchers based in the United States said they were able to "experience" the colour, which they named "olo", by firing laser pulses into their eyes using a device named after the Wizard of Oz. Olo cannot be seen with the naked eye, but the five people who have seen it describe it as being similar to teal. Professors from the University of California, Berkeley and the University of Washington School of Medicine published an article in the journal, Science Advances, on April 18 in which they put forth their discovery of a hue beyond the gamut of human vision. They explained that they had devised a technique called Oz, which can "trick" the human eye into seeing olo.


Alternation makes the adversary weaker in two-player games

Neural Information Processing Systems

Motivated by alternating game-play in two-player games, we study an altenating variant of the \textit{Online Linear Optimization} (OLO). In alternating OLO, a \textit{learner} at each round t \in [n] selects a vector x t and then an \textit{adversary} selects a cost-vector c t \in [-1,1] n . The learner then experiences cost (c t c {t-1}) \top x t instead of (c t) \top x t as in standard OLO. We establish that under this small twist, the \Omega(\sqrt{T}) lower bound on the regret is no longer valid. More precisely, we present two online learning algorithms for alternating OLO that respectively admit \mathcal{O}((\log n) {4/3} T {1/3}) regret for the n -dimensional simplex and \mathcal{O}(\rho \log T) regret for the ball of radius \rho 0 .


Coin Betting and Parameter-Free Online Learning

Neural Information Processing Systems

In the recent years, a number of parameter-free algorithms have been developed for online linear optimization over Hilbert spaces and for learning with expert advice. These algorithms achieve optimal regret bounds that depend on the unknown competitors, without having to tune the learning rates with oracle choices. We present a new intuitive framework to design parameter-free algorithms for both online linear optimization over Hilbert spaces and for learning with expert advice, based on reductions to betting on outcomes of adversarial coins. We instantiate it using a betting algorithm based on the Krichevsky-Trofimov estimator. The resulting algorithms are simple, with no parameters to be tuned, and they improve or match previous results in terms of regret guarantee and per-round complexity.


Sight Diagnostics raises $71 million for blood-testing computer vision

#artificialintelligence

This more than doubles the startup's total raised, and a spokesperson says it will be used to accelerate Sight's operations globally -- with a focus on the U.S. -- as Sight advances R&D for the detection of conditions like sepsis and cancer, as well as factors affecting COVID-19. Blood tests are generally unpleasant -- not to mention costly. On average, getting blood work done at a lab costs uninsured patients between $100 and $1,500. In the developing world, where the requisite equipment isn't always readily available, ancillary costs threaten to drive the price substantially higher. That's why Yossi Pollak, previously at Intel subsidiary Mobileye, and Daniel Levner, a former scientist at Harvard's Wyss Institute for Biologically Inspired Engineering, founded Sight Diagnostics in 2011.


Biotech AI startup Sight Diagnostics gets $27.8M to speed up blood tests

#artificialintelligence

Sight Diagnostics, an Israeli medical devices startup that's using AI technology to speed up blood testing, has closed a $27.8 million Series C funding round. The company has built a desktop machine, called OLO, that analyzes cartridges manually loaded with drops of the patient's blood -- performing blood counts in situ. The new funding is led by VC firm Longliv Ventures, also based in Israel, and a member of the multinational conglomerate CK Hutchison Group. Sight Diagnostics said it was after strategic investment for the Series C -- specifically investors that could contribute to its technological and commercial expansion. And on that front CK Hutchison Group's portfolio includes more than 14,500 health and beauty stores across Europe and Asia, providing a clear go-to-market route for the company's OLO blood testing device.


Coin Betting and Parameter-Free Online Learning

Neural Information Processing Systems

In the recent years, a number of parameter-free algorithms have been developed for online linear optimization over Hilbert spaces and for learning with expert advice. These algorithms achieve optimal regret bounds that depend on the unknown competitors, without having to tune the learning rates with oracle choices. We present a new intuitive framework to design parameter-free algorithms for both online linear optimization over Hilbert spaces and for learning with expert advice, based on reductions to betting on outcomes of adversarial coins. We instantiate it using a betting algorithm based on the Krichevsky-Trofimov estimator. The resulting algorithms are simple, with no parameters to be tuned, and they improve or match previous results in terms of regret guarantee and per-round complexity.