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We study adaptive regret bounds in terms of the variation of the losses (the so-called path-length bounds) for both multi-armed bandit and more generally linear bandit. We first show that the seemingly suboptimal path-length bound of (Wei…
We develop a novel and generic algorithm for the adversarial multi-armed bandit problem (or more generally the combinatorial semi-bandit problem). When instantiated differently, our algorithm achieves various new data-dependent regret…
This paper investigates to what extent one can improve reinforcement learning algorithms. Our study is split in three parts. First, our analysis shows that the classical asymptotic convergence rate $O(1/\sqrt{N})$ is pessimistic and can be…
Learning rate adaptation is a popular topic in machine learning. Gradient Descent trains neural nerwork with a fixed learning rate. Learning rate adaptation is proposed to accelerate the training process through adjusting the step size in…
This paper is motivated by recent research in the $d$-dimensional stochastic linear bandit literature, which has revealed an unsettling discrepancy: algorithms like Thompson sampling and Greedy demonstrate promising empirical performance,…
We define an online learning and optimization problem with discrete and irreversible decisions contributing toward a coverage target. In each period, a decision-maker selects facilities to open, receives information on the success of each…
One of the main obstacles to broad application of reinforcement learning methods is the parameter sensitivity of our core learning algorithms. In many large-scale applications, online computation and function approximation represent key…
We aim to design adaptive online learning algorithms that take advantage of any special structure that might be present in the learning task at hand, with as little manual tuning by the user as possible. A fundamental obstacle that comes up…
We study how to adapt to smoothly-varying ('easy') environments in well-known online learning problems where acquiring information is expensive. For the problem of label efficient prediction, which is a budgeted version of prediction with…
The level set estimation problem seeks to find all points in a domain ${\cal X}$ where the value of an unknown function $f:{\cal X}\rightarrow \mathbb{R}$ exceeds a threshold $\alpha$. The estimation is based on noisy function evaluations…
It has been experimentally observed in recent years that multi-layer artificial neural networks have a surprising ability to generalize, even when trained with far more parameters than observations. Is there a theoretical basis for this?…
We formalize the problem of machine unlearning as design of efficient unlearning algorithms corresponding to learning algorithms which perform a selection of adaptive queries from structured query classes. We give efficient unlearning…
We study model selection in linear bandits, where the learner must adapt to the dimension (denoted by $d_\star$) of the smallest hypothesis class containing the true linear model while balancing exploration and exploitation. Previous papers…
Reinforcement learning with multinomial logistic (MNL) function approximation has become an important framework due to its flexibility and broad applicability. While existing studies have established regret guarantees under worst-case…
Algorithms with predictions is a recent framework that has been used to overcome pessimistic worst-case bounds in incomplete information settings. In the context of scheduling, very recent work has leveraged machine-learned predictions to…
The {\em maximum cardinality} and {\em maximum weight matching} problems can be solved in time $\tilde{O}(m\sqrt{n})$, a bound that has resisted improvement despite decades of research. (Here $m$ and $n$ are the number of edges and…
We investigate the power of randomized algorithms for the maximum cardinality matching (MCM) and the maximum weight matching (MWM) problems in the online preemptive model. In this model, the edges of a graph are revealed one by one and the…
The analysis in Part I revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization when gradient noise is present. These algorithms are used when the risk functions are non-smooth and…
Machine learning assumes a pivotal role in our data-driven world. The increasing scale of models and datasets necessitates quick and reliable algorithms for model training. This dissertation investigates adaptivity in machine learning…
When a problem instance is perturbed by a small modification, one would hope to find a good solution for the new instance by building on a known good solution for the previous one. Via a rigorous mathematical analysis, we show that…