We consider the setting of prediction with expert advice; a learner makes predictions by aggregating those of a group of experts. Under this setting, and for the right choice of loss function and ``mixing'' algorithm, it is possible for the learner to achieve a constant regret regardless of the number of prediction rounds. For example, a constant regret can be achieved for \emph{mixable} losses using the \emph{aggregating algorithm}. The \emph{Generalized Aggregating Algorithm} (GAA) is a name for a family of algorithms parameterized by convex functions on simplices (entropies), which reduce to the aggregating algorithm when using the \emph{Shannon entropy} $\operatorname{S}$. For a given entropy $\Phi$, losses for which a constant regret is possible using the \textsc{GAA} are called $\Phi$-mixable. Which losses are $\Phi$-mixable was previously left as an open question. We fully characterize $\Phi$-mixability and answer other open questions posed by \cite{Reid2015}. We show that the Shannon entropy $\operatorname{S}$ is fundamental in nature when it comes to mixability; any $\Phi$-mixable loss is necessarily $\operatorname{S}$-mixable, and the lowest worst-case regret of the \textsc{GAA} is achieved using the Shannon entropy. Finally, by leveraging the connection between the \emph{mirror descent algorithm} and the update step of the GAA, we suggest a new \emph{adaptive} generalized aggregating algorithm and analyze its performance in terms of the regret bound.

For example, when solving RL problems such as Atari7 games, we may test different representation methods. Fortheaveragereward30 setting, it is still an open question whether S-bounds areachievable. Ourapproach canbeadapted totheepisodic31 case when the regret bounds would benefit from the improved bounds available in this setting. The A-dependence is optimal as for UCRL2, while the optimal dependence onS is still an open question (also46 for the MDP case). The optimal dependence on|Φ| in our setting is also open.

We thank reviewers for detailed comments and suggestions. We will address all comments in the revision. AIStats'19) considered the problem of learning an optimal action but ignored the contextual information. In this work, we incorporated the contextual information, which is readily available in many applications. The idea might look incremental.

Is Good Taste a Trap? The judgments we use to elevate our lives can also hem them in. In Belle Burden's memoir, " Strangers," she describes the end of her marriage. It happened suddenly: until learning of her husband's infidelity, through a voice mail from a stranger, she had no idea anything was wrong. Burden and her husband shared an apartment in Tribeca and a house on Martha's Vineyard.

Children and parked cars are color-coded on a monitor inside a Mercedes-Benz S-Class during an autonomous driving and AI demonstration in Immendingen, Germany on July 17, 2018. Children and parked cars are color-coded on a monitor inside a Mercedes-Benz S-Class during an autonomous driving and AI demonstration in Immendingen, Germany on July 17, 2018. In 2025, misconceptions about AI flourished as people struggled to make sense of the rapid development and adoption of the technology. Here are three popular ones to leave behind in the New Year. When GPT-5 was released in May, people wondered (not for the first time) if AI was hitting a wall.

This was supposed to be the year when autonomous agents took over everyday tasks. One year ago, Sam Altman, the C.E.O. of OpenAI, made a bold prediction: "We believe that, in 2025, we may see the first AI agents'join the workforce' and materially change the output of companies." A couple of weeks later, the company's chief product officer, Kevin Weil, said at the World Economic Forum conference at Davos in January, "I think 2025 is the year that we go from ChatGPT being this super smart thing . . . to ChatGPT doing things in the real world for you." He gave examples of artificial intelligence filling out online forms and booking restaurant reservations. He later promised, "We're going to be able to do that, no question."

Mathematically characterizing the implicit regularization induced by gradient-based optimization is a longstanding pursuit in the theory of deep learning. A widespread hope is that a characterization based on minimization of norms may apply, and a standard test-bed for studying this prospect is matrix factorization (matrix completion via linear neural networks). It is an open question whether norms can explain the implicit regularization in matrix factorization. The current paper resolves this open question in the negative, by proving that there exist natural matrix factorization problems on which the implicit regularization drives all norms (and quasi-norms) towards infinity. Our results suggest that, rather than perceiving the implicit regularization via norms, a potentially more useful interpretation is minimization of rank. We demonstrate empirically that this interpretation extends to a certain class of non-linear neural networks, and hypothesize that it may be key to explaining generalization in deep learning.

Can You Reclaim Your Mind? To feel mentally alive, you have to do more than defeat distraction. Looking back over the columns I've written in 2025, I can see that a lot of them, broadly construed, have been about reclaiming one's mind. I wrote about living in the present, picturing the future, and exploring one's memories; about reading, learning, and making the most of one's spare time; and about whether artificial intelligence will end up expanding our thinking or limiting it . The shared subject was resistance to the forces, malevolent or inertial, that can render us mentally exhausted and scattered.

Is Cognitive Dissonance Actually a Thing? In 1934, an 8.0-magnitude earthquake hit eastern India, killing thousands and devastating several cities. Curiously, in areas that were spared the worst destruction, stories soon spread that an even bigger disaster was on its way. Leon Festinger, a young American psychologist at the University of Minnesota, read about these rumors in the early nineteen-fifties and was puzzled. Festinger didn't think people would voluntarily adopt anxiety-inducing ideas. Instead, he reasoned, the rumors could better be described as "anxiety justifying." Some had felt the earth shake and were overwhelmed with fear. When the outcome--they were spared--didn't match their emotions, they embraced predictions that affirmed their fright.