We introduce Cautious Optimism, a framework for substantially faster regularized learning in general games. Cautious Optimism, as a variant of Optimism, adaptively controls the learning pace in a dynamic, non-monotone manner to accelerate no-regret learning dynamics. Cautious Optimism takes as input any instance of Follow-the-Regularized-Leader (FTRL) and outputs an accelerated no-regret learning algorithm (COFTRL) by pacing the underlying FTRL with minimal computational overhead. Importantly, it retains uncoupledness, that is, learners do not need to know other players' utilities. Cautious Optimistic FTRL (COFTRL) achieves near-optimal $O_T(\log T)$ regret in diverse self-play (mixing and matching regularizers) while preserving the optimal $O_T(\sqrt{T})$ regret in adversarial scenarios. In contrast to prior works (e.g., Syrgkanis et al. [2015], Daskalakis et al. [2021]), our analysis does not rely on monotonic step sizes, showcasing a novel route for fast learning in general games. Moreover, instances of COFTRL achieve new state-of-the-art regret minimization guarantees in general convex games, exponentially improving the dependence on the dimension of the action space $d$ over previous works [Farina et al., 2022a].

We establish the first uncoupled learning algorithm that attains $O(n \log^2 d \log T)$ per-player regret in multi-player general-sum games, where $n$ is the number of players, $d$ is the number of actions available to each player, and $T$ is the number of repetitions of the game. Our results exponentially improve the dependence on $d$ compared to the $O(n\, d \log T)$ regret attainable by Log-Regularized Lifted Optimistic FTRL [Far+22c], and also reduce the dependence on the number of iterations $T$ from $\log^4 T$ to $\log T$ compared to Optimistic Hedge, the previously well-studied algorithm with $O(n \log d \log^4 T)$ regret [DFG21]. Our algorithm is obtained by combining the classic Optimistic Multiplicative Weights Update (OMWU) with an adaptive, non-monotonic learning rate that paces the learning process of the players, making them more cautious when their regret becomes too negative.

When is it a bad idea to bet on the future? First, we're seeing massive shifts in customer behavior during the pandemic -- behaviors that look likely to last. Second, the emergence of Millennials and Gen Z as significant market segments suggest that those new behaviors are just the beginning. Third, and most importantly, the big guys of digital -- Apple, Facebook, Google, Amazon, and Microsoft -- are all placing big bets that threaten to reshape the landscape for every business in due time. So, maybe a better question is "How can you bet on the future to win?" We'll take a look at who's leading the way towards the future, some useful frameworks for how to think about betting on the future, and how to place smart bets for your business… bets that you can win. Here are the show notes for you. Here are the regular show notes detailing links and news related to this week's episode.

Phase I clinical trials are designed to test the safety (non-toxicity) of drugs and find the maximum tolerated dose (MTD). This task becomes significantly more challenging when multiple-drug dose-combinations (DC) are involved, due to the inherent conflict between the exponentially increasing DC candidates and the limited patient budget. This paper proposes a novel Bayesian design, SDF-Bayes, for finding the MTD for drug combinations in the presence of safety constraints. Rather than the conventional principle of escalating or de-escalating the current dose of one drug (perhaps alternating between drugs), SDF-Bayes proceeds by cautious optimism: it chooses the next DC that, on the basis of current information, is most likely to be the MTD (optimism), subject to the constraint that it only chooses DCs that have a high probability of being safe (caution). We also propose an extension, SDF-Bayes-AR, that accounts for patient heterogeneity and enables heterogeneous patient recruitment. Extensive experiments based on both synthetic and real-world datasets demonstrate the advantages of SDF-Bayes over state of the art DC trial designs in terms of accuracy and safety.

"Also, ain't no rule says a dog can't play basketball." SAN FRANCISCO -- President-elect Donald Trump has vowed to make America great again. But if the sentiments of tech workers and the general public are any indication of what he's about to face in the White House, he has a split country to stitch together. Such is the onerous task he inherits, based on a new study measuring the viewpoints of 500 "Tech Elites," defined as people who work or invest in the technology sector, and 1,000 members of the U.S. "General Population." For starters, 65% of tech elites believe innovation is going in the right direction, compared with just 46% in the general public (33% say they don't know).