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Register a new userBandits with adversarial scaling
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Thodoris Lykouris
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We study adversarial scaling, a multi-armed bandit model where rewards have a stochastic and an adversarial component. Our model captures display advertising where the click-through-rate can be decomposed to a (fixed across time) arm-quality component and a non-stochastic user-relevance component (fixed across arms). Despite the relative stochasticity of our model, we demonstrate two settings where most bandit algorithms suffer. On the positive side, we show that two algorithms, one from the action elimination and one from the mirror descent family are adaptive enough to be robust to adversarial scaling. Our results shed light on the robustness of adaptive parameter selection in stochastic bandits, which may be of independent interest.
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This paper investigates the adversarial Bandits with Knapsack (BwK) online learning problem, where a player repeatedly chooses to perform an action, pays the corresponding cost, and receives a reward associated with the action. The player is constrained by the maximum budget $B$ that can be spent to perform actions, and the rewards and the costs of the actions are assigned by an adversary. This problem has only been studied in the restricted setting where the reward of an action is greater than the cost of the action, while we provide a solution in the general setting. Namely, we propose EXP3.BwK, a novel algorithm that achieves order optimal regret. We also propose EXP3++.BwK, which is order optimal in the adversarial BwK setup, and incurs an almost optimal expected regret with an additional factor of $log(B)$ in the stochastic BwK setup. Finally, we investigate the case of having large costs for the actions (i.e., they are comparable to the budget size $B$), and show that for the adversarial setting, achievable regret bounds can be significantly worse, compared to the case of having costs bounded by a constant, which is a common assumption within the BwK literature.
Consider a player that in each round $t$ out of $T$ rounds chooses an action and observes the incurred cost after a delay of $d_{t}$ rounds. The cost functions and the delay sequence are chosen by an adversary. We show that even if the players algorithms lose their no regret property due to too large delays, the expected discounted ergodic distribution of play converges to the set of coarse correlated equilibrium (CCE) if the algorithms have no discounted-regret. For a zero-sum game, we show that no discounted-regret is sufficient for the discounted ergodic average of play to converge to the set of Nash equilibria. We prove that the FKM algorithm with $n$ dimensions achieves a regret of $Oleft(nT^{frac{3}{4}}+sqrt{n}T^{frac{1}{3}}D^{frac{1}{3}}right)$ and the EXP3 algorithm with $K$ arms achieves a regret of $Oleft(sqrt{ln Kleft(KT+Dright)}right)$ even when $D=sum_{t=1}^{T}d_{t}$ and $T$ are unknown. These bounds use a novel doubling trick that provably retains the regret bound for when $D$ and $T$ are known. Using these bounds, we show that EXP3 and FKM have no discounted-regret even for $d_{t}=Oleft(tlog tright)$. Therefore, the CCE of a finite or convex unknown game can be approximated even when only delayed bandit feedback is available via simulation.
We consider a fully decentralized multi-player stochastic multi-armed bandit setting where the players cannot communicate with each other and can observe only their own actions and rewards. The environment may appear differently to different players, $textit{i.e.}$, the reward distributions for a given arm are heterogeneous across players. In the case of a collision (when more than one player plays the same arm), we allow for the colliding players to receive non-zero rewards. The time-horizon $T$ for which the arms are played is emph{not} known to the players. Within this setup, where the number of players is allowed to be greater than the number of arms, we present a policy that achieves near order-optimal expected regret of order $O(log^{1 + delta} T)$ for some $0 < delta < 1$ over a time-horizon of duration $T$. This paper is currently under review at IEEE Transactions on Information Theory.
We reconsider the training objective of Generative Adversarial Networks (GANs) from the mixed Nash Equilibria (NE) perspective. Inspired by the classical prox methods, we develop a novel algorithmic framework for GANs via an infinite-dimensional two-player game and prove rigorous convergence rates to the mixed NE, resolving the longstanding problem that no provably convergent algorithm exists for general GANs. We then propose a principled procedure to reduce our novel prox methods to simple sampling routines, leading to practically efficient algorithms. Finally, we provide experimental evidence that our approach outperforms methods that seek pure strategy equilibria, such as SGD, Adam, and RMSProp, both in speed and quality.
We derive improved regret bounds for the Tsallis-INF algorithm of Zimmert and Seldin (2021). We show that in adversarial regimes with a $(Delta,C,T)$ self-bounding constraint the algorithm achieves $mathcal{O}left(left(sum_{i eq i^*} frac{1}{Delta_i}right)log_+left(frac{(K-1)T}{left(sum_{i eq i^*} frac{1}{Delta_i}right)^2}right)+sqrt{Cleft(sum_{i eq i^*}frac{1}{Delta_i}right)log_+left(frac{(K-1)T}{Csum_{i eq i^*}frac{1}{Delta_i}}right)}right)$ regret bound, where $T$ is the time horizon, $K$ is the number of arms, $Delta_i$ are the suboptimality gaps, $i^*$ is the best arm, $C$ is the corruption magnitude, and $log_+(x) = maxleft(1,log xright)$. The regime includes stochastic bandits, stochastically constrained adversarial bandits, and stochastic bandits with adversarial corruptions as special cases. Additionally, we provide a general analysis, which allows to achieve the same kind of improvement for generalizations of Tsallis-INF to other settings beyond multiarmed bandits.
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