There exists constantsC1,C2,C3,C4 depending onψ such that the following holds true.

Continual Learning (CL) poses a significant challenge in Artificial Intelligence, aiming to mirror the human ability to incrementally acquire knowledge and skills. While extensive research has focused on CL within the context of classification tasks, the advent of increasingly powerful generative models necessitates the exploration of Continual Learning of Generative models (CLoG). This paper advocates for shifting the research focus from classification-based CL to CLoG. We systematically identify the unique challenges presented by CLoG compared to traditional classification-based CL. We adapt three types of existing CL methodologies, replay-based, regularization-based, and parameter-isolation-based methods to generative tasks and introduce comprehensive benchmarks for CLoG that feature great diversity and broad task coverage. Our benchmarks and results yield intriguing insights that can be valuable for developing future CLoG methods. Additionally, we will release a codebase designed to facilitate easy benchmarking and experimentation in CLoG publicly at https://github.com/linhaowei1/CLoG. We believe that shifting the research focus to CLoG will benefit the continual learning community and illuminate the path for next-generation AI-generated content (AIGC) in a lifelong learning paradigm.

We consider the problem of estimating the mean of a random vector based on $N$ independent, identically distributed observations. We prove the existence of an estimator that has a near-optimal error in all directions in which the variance of the one dimensional marginal of the random vector is not too small: with probability $1-\delta$, the procedure returns $\wh{\mu}_N$ which satisfies that for every direction $u \in S^{d-1}$, \[ \inr{\wh{\mu}_N - \mu, u}\le \frac{C}{\sqrt{N}} \left( \sigma(u)\sqrt{\log(1/\delta)} + \left(\E\|X-\EXP X\|_2^2\right)^{1/2} \right)~, \] where $\sigma^2(u) = \var(\inr{X,u})$ and $C$ is a constant. To achieve this, we require only slightly more than the existence of the covariance matrix, in the form of a certain moment-equivalence assumption. The proof relies on novel bounds for the ratio of empirical and true probabilities that hold uniformly over certain classes of random variables.

When my children were young, we had a toy that they assembled consisting of seventy-five plastic interconnecting tunnel pieces, including having numerous tall ramps and winding paths, and when a marble was dropped into the topmost funnel it would be of great delight to all as we watched the marble roll throughout the structure. It was advertised via a slogan that said down the tube it goes, where the marble stops, nobody knows, and presumably helped teach my children about physics (well, it was actually mainly just a lot of fun). Being quite rambunctious, the kids sought out new ways to test the capabilities and limits of the toy. Putting one marble down the shoot was fun. Perhaps putting two marbles would be twice the fun! They tried this and it made them squeal with delight. If two marbles are twice the fun, certainly four marbles would quadruple the fun. They kept increasing the number of marbles and with each such increment the plastic contraption would shake and shimmy more so. How many marbles would the system withstand?

We consider the problem of bandit optimization, inspired by stochastic optimization and online learning problems with bandit feedback. In this problem, the objective is to minimize a global loss function of all the actions, not necessarily a cumulative loss. This framework allows us to study a very general class of problems, with applications in statistics, machine learning, and other fields. To solve this problem, we analyze the Upper-Confidence Frank-Wolfe algorithm, inspired by techniques for bandits and convex optimization. We give theoretical guarantees for the performance of this algorithm over various classes of functions, and discuss the optimality of these results.

Cécile B. Evans, How happy a Thing Can Be, 2014. The word'automation' is appearing in places that would have seemed unlikely to most people less than a decade ago: journalism, art, design or law. Robots and algorithms are being increasingly convincing at doing things just like humans. The Promise of Total Automation, an exhibition recently opened at Kunsthalle Wien in Vienna, looks at our troubled relationship with machines. Technical devices that were originally designed to serve and assist us and are now getting smarter and harder to control and comprehend.

We consider stochastic multi-armed bandits where the expected reward is a unimodal function over partially ordered arms. This important class of problems has been recently investigated in (Cope 2009, Yu 2011). The set of arms is either discrete, in which case arms correspond to the vertices of a finite graph whose structure represents similarity in rewards, or continuous, in which case arms belong to a bounded interval. For discrete unimodal bandits, we derive asymptotic lower bounds for the regret achieved under any algorithm, and propose OSUB, an algorithm whose regret matches this lower bound. Our algorithm optimally exploits the unimodal structure of the problem, and surprisingly, its asymptotic regret does not depend on the number of arms. We also provide a regret upper bound for OSUB in non-stationary environments where the expected rewards smoothly evolve over time. The analytical results are supported by numerical experiments showing that OSUB performs significantly better than the state-of-the-art algorithms. For continuous sets of arms, we provide a brief discussion. We show that combining an appropriate discretization of the set of arms with the UCB algorithm yields an order-optimal regret, and in practice, outperforms recently proposed algorithms designed to exploit the unimodal structure.