Universities have become generic, one professor and former dean argues. In the A.I. era, students may demand something they can't get elsewhere. Last week, I asked whether, as a forty-six-year-old father of two, I should keep contributing to my children's college funds, or if perhaps some combination of anti-establishment fervor, A.I., and a shifting economy could save me some money. I don't have a particularly good answer yet, at least not one good enough to inspire the purchase of a midlife-crisis car, my son's and daughter's futures be damned. But, after wrestling with that query in Part 1 of what will be a series of articles, I think there may be a better one to ask. The question is not, I think, "How will A.I. change higher education?" I wanted to talk with someone who stood outside the polite consensus which holds that college as we know it will survive, if only because, as I wrote last week, humans will always want to differentiate their children from other people's children.

Consider betting against a sequence of data in $[0,1]$, where one is allowed to make any bet that is fair if the data have a conditional mean $m_0 \in (0,1)$. Cover's universal portfolio algorithm delivers a worst-case regret of $O(\ln n)$ compared to the best constant bet in hindsight, and this bound is unimprovable against adversarially generated data. In this work, we present a novel mixture betting strategy that combines insights from Robbins and Cover, and exhibits a different behavior: it eventually produces a regret of $O(\ln \ln n)$ on \emph{almost} all paths (a measure-one set of paths if each conditional mean equals $m_0$ and intrinsic variance increases to $\infty$), but has an $O(\log n)$ regret on the complement (a measure zero set of paths). Our paper appears to be the first to point out the value in hedging two very different strategies to achieve a best-of-both-worlds adaptivity to stochastic data and protection against adversarial data. We contrast our results to those in~\cite{agrawal2025regret} for a sub-Gaussian mixture on unbounded data: their worst-case regret has to be unbounded, but a similar hedging delivers both an optimal betting growth-rate and an almost sure $\ln\ln n$ regret on stochastic data. Finally, our strategy witnesses a sharp game-theoretic upper law of the iterated logarithm, analogous to~\cite{shafer2005probability}.

The population $\mathrm{KL}_{\inf}$ is a fundamental quantity that appears in lower bounds for (asymptotically) optimal regret of pure-exploration stochastic bandit algorithms, and optimal stopping time of sequential tests. Motivated by this, an empirical $\mathrm{KL}_{\inf}$ statistic is frequently used in the design of (asymptotically) optimal bandit algorithms and sequential tests. While nonasymptotic concentration bounds for the empirical $\mathrm{KL}_{\inf}$ have been developed, their optimality in terms of constants and rates is questionable, and their generality is limited (usually to bounded observations). The fundamental limits of nonasymptotic concentration are often described by the asymptotic fluctuations of the statistics. With that motivation, this paper presents a tight (upper and lower) law of the iterated logarithm for empirical $\mathrm{KL}_{\inf}$ applying to extremely general (unbounded) data.

Winners will emerge from the Artificial Intelligence (AI) boom, but there will be carnage along the way, the boss of a US tech giant has warned. Chuck Robbins, chairman and chief executive of Cisco Systems, told the BBC the technology will be bigger than the internet, but the current market is probably a bubble and some companies won't make it. Cisco, one of the world's leading technology companies, is behind some of the critical IT infrastructure enabling day-to-day use of AI. Robbins said some jobs will be changed, or even eliminated, by AI, particularly in areas like customer services where companies will need fewer people, but urged workers to embrace, not fear, the technology. His comments follow a series of warnings over the recent surge in investment in AI, with some claiming the sector amounts to a bubble set to burst, rocking markets and bankrupting companies.

We study the problem of minimising regret in two-armed bandit problems with Gaussian rewards. Our objective is to use this simple setting to illustrate that strategies based on an exploration phase (up to a stopping time) followed by exploitation are necessarily suboptimal. The results hold regardless of whether or not the difference in means between the two arms is known.

We present a universal framework for constructing confidence sets based on sequential likelihood mixing. Building upon classical results from sequential analysis, we provide a unifying perspective on several recent lines of work, and establish fundamental connections between sequential mixing, Bayesian inference and regret inequalities from online estimation. The framework applies to any realizable family of likelihood functions and allows for non-i.i.d. data and anytime validity. Moreover, the framework seamlessly integrates standard approximate inference techniques, such as variational inference and sampling-based methods, and extends to misspecified model classes, while preserving provable coverage guarantees. We illustrate the power of the framework by deriving tighter confidence sequences for classical settings, including sequential linear regression and sparse estimation, with simplified proofs.

In this memorial paper, we honor Tze Leung Lai's seminal contributions to the topic of multi-armed bandits, with a specific focus on his pioneering work on the upper confidence bound. We establish sharp non-asymptotic regret bounds for an upper confidence bound index with a constant level of exploration for Gaussian rewards. Furthermore, we establish a non-asymptotic regret bound for the upper confidence bound index of Lai (1987) which employs an exploration function that decreases with the sample size of the corresponding arm. The regret bounds have leading constants that match the Lai-Robbins lower bound. Our results highlight an aspect of Lai's seminal works that deserves more attention in the machine learning literature.

Kyle Jensen, the director of Arizona State University's writing programs, is gearing up for the fall semester. The responsibility is enormous: Each year, 23,000 students take writing courses under his oversight. The teachers' work is even harder today than it was a few years ago, thanks to AI tools that can generate competent college papers in a matter of seconds. A mere week after ChatGPT appeared in November 2022, The Atlantic declared that "The College Essay Is Dead." Two school years later, Jensen is done with mourning and ready to move on.

We study the problem of minimising regret in two-armed bandit problems with Gaussian rewards. Our objective is to use this simple setting to illustrate that strategies based on an exploration phase (up to a stopping time) followed by exploitation are necessarily suboptimal. The results hold regardless of whether or not the difference in means between the two arms is known. Besides the main message, we also refine existing deviation inequalities, which allow us to design fully sequential strategies with finite-time regret guarantees that are (a) asymptotically optimal as the horizon grows and (b) order-optimal in the minimax sense. Furthermore we provide empirical evidence that the theory also holds in practice and discuss extensions to non-gaussian and multiple-armed case.

Alec Robbins spent weeks thinking about anuses. It was fall 2022, and Robbins, a cartoonist and game designer by trade, had been given a curious task: design an egg character for a video game to be played on Netflix's sketch comedy series I Think You Should Leave. And there was one part of the character that had to be just right for the gag to land. In the bit, show creator Tim Robinson was going to be playing an office worker goofing around on a (fake) vintage Mac game where the goal was to feed eggs to a bigger egg. Land enough eggs in his mouth and the anthropomorphized egg would reward the triumphant player with a peep show. Thus, Robbins' butthole had to look like a real prize.