Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring

• URL: http://arxiv.org/abs/2402.08321v2
• Date: Sun, 16 Feb 2025 19:23:06 GMT
• Title: Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring
• Authors: Taira Tsuchiya, Shinji Ito, Junya Honda,
• Abstract summary: Partial monitoring is a generic framework of online decision-making problems with limited feedback. We present a new framework and analysis for ExO with a hybrid regularizer. In particular, we derive a regret bound of $O(sum_a neq a*)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds.
• Score: 41.20252349191698
• License:
• Abstract: Partial monitoring is a generic framework of online decision-making problems with limited feedback. To make decisions from such limited feedback, it is necessary to find an appropriate distribution for exploration. Recently, a powerful approach for this purpose, \emph{exploration by optimization} (ExO), was proposed, which achieves optimal bounds in adversarial environments with follow-the-regularized-leader for a wide range of online decision-making problems. However, a naive application of ExO in stochastic environments significantly degrades regret bounds. To resolve this issue in locally observable games, we first establish a new framework and analysis for ExO with a hybrid regularizer. This development allows us to significantly improve existing regret bounds of best-of-both-worlds (BOBW) algorithms, which achieves nearly optimal bounds both in stochastic and adversarial environments. In particular, we derive a stochastic regret bound of $O(\sum_{a \neq a^*} k^2 m^2 \log T / \Delta_a)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds, $a^*$ is an optimal action, and $\Delta_a$ is the suboptimality gap for action $a$. This bound is roughly $\Theta(k^2 \log T)$ times smaller than existing BOBW bounds. In addition, for globally observable games, we provide a new BOBW algorithm with the first $O(\log T)$ stochastic bound.

Related papers

• Beyond Minimax Rates in Group Distributionally Robust Optimization via a Novel Notion of Sparsity [14.396304498754688]
  We show a novel notion of sparsity that we dub $(lambda, beta)$-sparsity. In short, there is a set of at most $beta$ groups whose risks at $theta$ all are at least $lambda$ larger than the risks of the other groups. We show how to get a dimension-free semi-adaptive sample complexity bound with a computationally efficient method.
  arXiv  Detail & Related papers  (2024-10-01T13:45:55Z)
• Nearly Minimax Optimal Regret for Learning Linear Mixture Stochastic Shortest Path [80.60592344361073]
  We study the Shortest Path (SSP) problem with a linear mixture transition kernel. An agent repeatedly interacts with a environment and seeks to reach certain goal state while minimizing the cumulative cost. Existing works often assume a strictly positive lower bound of the iteration cost function or an upper bound of the expected length for the optimal policy.
  arXiv  Detail & Related papers  (2024-02-14T07:52:00Z)
• Combinatorial Stochastic-Greedy Bandit [79.1700188160944]
  We propose a novelgreedy bandit (SGB) algorithm for multi-armed bandit problems when no extra information other than the joint reward of the selected set of $n$ arms at each time $tin [T]$ is observed. SGB adopts an optimized-explore-then-commit approach and is specifically designed for scenarios with a large set of base arms.
  arXiv  Detail & Related papers  (2023-12-13T11:08:25Z)
• Contextual Decision-Making with Knapsacks Beyond the Worst Case [5.65888994172721]
  We study the framework of a dynamic decision-making scenario with resource constraints. In this framework, an agent selects an action in each round upon observing a random request. We prove that our algorithm maintains a near-optimal $widetildeO(sqrtT)$ regret even in the worst cases.
  arXiv  Detail & Related papers  (2022-11-25T08:21:50Z)
• Towards Painless Policy Optimization for Constrained MDPs [46.12526917024248]
  We study policy optimization in an infinite horizon, $gamma$-discounted constrained Markov decision process (CMDP) Our objective is to return a policy that achieves large expected reward with a small constraint violation. We propose a generic primal-dual framework that allows us to bound the reward sub-optimality and constraint violation for arbitrary algorithms.
  arXiv  Detail & Related papers  (2022-04-11T15:08:09Z)
• Bayesian Optimistic Optimisation with Exponentially Decaying Regret [58.02542541410322]
  The current practical BO algorithms have regret bounds ranging from $mathcalO(fraclogNsqrtN)$ to $mathcal O(e-sqrtN)$, where $N$ is the number of evaluations. This paper explores the possibility of improving the regret bound in the noiseless setting by intertwining concepts from BO and tree-based optimistic optimisation. We propose the BOO algorithm, a first practical approach which can achieve an exponential regret bound with order $mathcal O(N-sqrt
  arXiv  Detail & Related papers  (2021-05-10T13:07:44Z)
• Fine-Grained Gap-Dependent Bounds for Tabular MDPs via Adaptive Multi-Step Bootstrap [84.66885506098724]
  This paper presents a new model-free algorithm for episodic finite-horizon Markov Decision Processes (MDP), Adaptive Multi-step Bootstrap (AMB) We show AMB achieves a gap-dependent regret bound that only scales with the sum of the inverse of the sub-optimality gaps. We also show AMB suffers an additional $frac|Z_mul|Delta_min$ regret, where $Z_mul$ is the set of state-action pairs $(s,a)$'s satisfying $a$ is a non-unique optimal action for
  arXiv  Detail & Related papers  (2021-02-09T07:46:34Z)
• Near-Optimal Regret Bounds for Contextual Combinatorial Semi-Bandits with Linear Payoff Functions [53.77572276969548]
  We show that the C$2$UCB algorithm has the optimal regret bound $tildeO(dsqrtkT + dk)$ for the partition matroid constraints. For general constraints, we propose an algorithm that modifies the reward estimates of arms in the C$2$UCB algorithm.
  arXiv  Detail & Related papers  (2021-01-20T04:29:18Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.