Mashable Voices Look Up Trending Now Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Say More Mashable Selects Safety Net Versus Gift Ideas For Everyone On Your List Switch Off In My Bag VidCon with Mashable All Series Matt Ford is a freelance contributor to Mashable. All products featured here are independently selected by our editors and writers. If you buy something through links on our site, Mashable may earn an affiliate commission. Deal pricing and availability subject to change after time of publication. Learn more about how we select deals .

Trending Now Look Up Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Say More Mashable Selects Mashable Voices Safety Net Creator Hub Versus Gift Ideas For Everyone On Your List Switch Off In My Bag All Series You do need to act fast to score Pokémon TCG deals. Matt Ford is a freelance contributor to Mashable. All products featured here are independently selected by our editors and writers. If you buy something through links on our site, Mashable may earn an affiliate commission. Deal pricing and availability subject to change after time of publication.

Look Up Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Say More Safety Net Creator Hub Versus Gift Ideas For Everyone On Your List Mashable Selects Switch Off Trending Now In My Bag VidCon with Mashable All Series Here are some tips and tricks to help you find the answer to Wordle #1887. Can't get enough of Wordle? Today's answer should be easy to solve if you have a preference between charcoal or natural gas. If you just want to be told today's word, you can jump to the bottom of this article for today's solution revealed. But if you'd rather solve it yourself, keep reading for some clues, tips, and strategies to assist you.

Look Up Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Say More Safety Net Creator Hub Versus Gift Ideas For Everyone On Your List Mashable Selects Switch Off Trending Now In My Bag VidCon with Mashable All Series Amazon's price is now only just above TCGplayer's $123.21 market price. Ben Williams is a freelance writer at Mashable, having joined the team in June 2025. With over 10 years experience in gaming, tech, TV, anime, and film, there's nothing he hasn't covered. Alongside Ben's other work at IGN, Radio Times, Eurogamer, UNILAD Tech, and Rock Paper Shotgun, he also has bylines at sites like GamesRadar+, PCGamesN, ScreenSphere, Twinfinite, ScreenRant, GGRecon, and more. All products featured here are independently selected by our editors and writers.

Look Up Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Say More Safety Net Creator Hub Versus Gift Ideas For Everyone On Your List Mashable Selects Switch Off Trending Now In My Bag VidCon with Mashable All Series This deal is even beating TCGplayer. Ben Williams is a freelance writer at Mashable, having joined the team in June 2025. With over 10 years experience in gaming, tech, TV, anime, and film, there's nothing he hasn't covered. Alongside Ben's other work at IGN, Radio Times, Eurogamer, UNILAD Tech, and Rock Paper Shotgun, he also has bylines at sites like GamesRadar+, PCGamesN, ScreenSphere, Twinfinite, ScreenRant, GGRecon, and more. All products featured here are independently selected by our editors and writers.

Look Up Safety Net Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Creator Hub Versus Say More Gift Ideas For Everyone On Your List Mashable Selects Switch Off Trending Now In My Bag VidCon with Mashable All Series Everything you need to know to beat the scalpers. Ben Williams is a freelance writer at Mashable, having joined the team in June 2025. With over 10 years experience in gaming, tech, TV, anime, and film, there's nothing he hasn't covered. Alongside Ben's other work at IGN, Radio Times, Eurogamer, UNILAD Tech, and Rock Paper Shotgun, he also has bylines at sites like GamesRadar+, PCGamesN, ScreenSphere, Twinfinite, ScreenRant, GGRecon, and more. All products featured here are independently selected by our editors and writers.

Total Solar Eclipse 2024 Look Up Mashable Selects Say More Versus Creator Hub Switch Off Mashable's Best: E-readers, robovacs, laptops, earbuds, smart home and more Trending Now Safety Net In My Bag VidCon with Mashable All Series Though TCGplayer is still the cheapest place to buy. Ben Williams is a freelance writer at Mashable, having joined the team in June 2025. With over 10 years experience in gaming, tech, TV, anime, and film, there's nothing he hasn't covered. Alongside Ben's other work at IGN, Radio Times, Eurogamer, UNILAD Tech, and Rock Paper Shotgun, he also has bylines at sites like GamesRadar+, PCGamesN, ScreenSphere, Twinfinite, ScreenRant, GGRecon, and more. All products featured here are independently selected by our editors and writers.

We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully censored feedback, we introduce an action-dependent feedback model inspired by real limit order books: when a trade occurs, the trader's valuation remains hidden, whereas when no trade occurs, informative feedback about supply and demand is revealed. We show that this additional information fundamentally changes the learnability of the problem. In the stochastic setting with i.i.d. market prices, we propose an elimination-based algorithm that achieves $O(\sqrt T)$ regret with high probability, without requiring any smoothness assumptions on the distribution of trader valuations. We then extend this result to a broad class of mean-reverting price processes by considering both local, autoregressive dynamics and a weaker global drift condition based on cumulative deviations from the mean. Under either assumption, we establish high-probability $O(\sqrt T)$ regret bounds, relying on a new concentration inequality of independent interest. Finally, in the adversarial setting with oblivious prices, we design an explore-then-perturb algorithm that guarantees $O(T^{2/3})$ regret in expectation. Our results quantify the value of observing the order book in online market making and demonstrate that even limited, action-dependent feedback can substantially improve regret guarantees compared to standard bandit feedback models.

In this section, we provide more information on the application backgrounds, including the detailed structures of the RAS and VAS, the structures of the simulated advertising system. We also discuss the importance and universality of the IBOO problem in auto-bidding, which acts as the motivation of this work.