We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previous best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous best algorithm and show a consistent exponential improvement in several different scenarios.

We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previous best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than \Omega(\sqrt{T}) . We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in O(\log T), an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous best algorithm and show a consistent exponential improvement in several different scenarios.

It is well known that modern deep neural networks are powerful enough to memorize datasets even when the labels have been randomized. Recently, Vershynin(2020) settled a long standing question by Baum(1988), proving that deep threshold networks can memorize n points in d dimensions using \widetilde{\mathcal{O}}(e {1/\delta 2} \sqrt{n}) neurons and \widetilde{\mathcal{O}}(e {1/\delta 2}(d \sqrt{n}) n) weights, where \delta is the minimum distance between the points. Our construction uses Gaussian random weights only in the first layer, while all the subsequent layers use binary or integer weights. We also prove new lower bounds by connecting memorization in neural networks to the purely geometric problem of separating n points on a sphere using hyperplanes.

In this paper, we study gap-dependent regret guarantees for risk-sensitive reinforcement learning based on the entropic risk measure. We propose a novel definition of sub-optimality gaps, which we call cascaded gaps, and we discuss their key components that adapt to the underlying structures of the problem. Based on the cascaded gaps, we derive non-asymptotic and logarithmic regret bounds for two model-free algorithms under episodic Markov decision processes. We show that, in appropriate settings, these bounds feature exponential improvement over existing ones that are independent of gaps. We also prove gap-dependent lower bounds, which certify the near optimality of the upper bounds.

We study revenue optimization learning algorithms for posted-price auctions with strategic buyers. We analyze a very broad family of monotone regret minimization algorithms for this problem, which includes the previous best known algorithm, and show that no algorithm in that family admits a strategic regret more favorable than $\Omega(\sqrt{T})$. We then introduce a new algorithm that achieves a strategic regret differing from the lower bound only by a factor in $O(\log T)$, an exponential improvement upon the previous best algorithm. Our new algorithm admits a natural analysis and simpler proofs, and the ideas behind its design are general. We also report the results of empirical evaluations comparing our algorithm with the previous best algorithm and show a consistent exponential improvement in several different scenarios.

How might law firms harness the transformational potential of technological change to drive exponential business growth? We are at the start of a Fourth Industrial Revolution--a wave of transformation fueled by powerful technologies such as artificial intelligence (AI). This could drive a bigger wave of growth in the legal sector than any other change in history. Previous transformations gave us steam-based mechanization, electrification and mass production, and then electronics, information technology, and automation. This new era of smart machines is fueled by exponential improvement and convergence of multiple scientific and technological fields.

The 2016 victory by a Google-built AI at the notoriously complex game of Go was a bold demonstration of the power of modern machine learning. That triumphant AlphaGo system, created by AI research group Google DeepMind, confounded expectations that computers were years away from beating a human champion. But as significant as that achievement was, DeepMind's co-founder Demis Hassabis expects it will be dwarfed by how AI will transform society in the years to come. "I would actually be very pessimistic about the world if something like AI wasn't coming down the road," he said. "The reason I say that is that if you look at the challenges that confront society: climate change, sustainability, mass inequality -- which is getting worse -- diseases, and healthcare, we're not making progress anywhere near fast enough in any of these areas. "Either we need an exponential improvement in human behavior -- less selfishness, less short-termism, more collaboration, more generosity -- or we need an exponential improvement in technology.