Raymond Zhang

Raymond Zhang, Hédi Hadiji, Richard Combes

We consider the maximization of $x^\top θ$ over $(x,θ) \in \mathcal{X} \times Θ$, with $\mathcal{X} \subset \mathbb{R}^d$ convex and $Θ\subset \mathbb{R}^d$ an ellipsoid. This problem is fundamental in linear bandits, as the learner must solve it at every time step using optimistic algorithms. We first show that for some sets $\mathcal{X}$ e.g. $\ell_p$ balls with $p>2$, no efficient algorithms exist unless $\mathcal{P} = \mathcal{NP}$. We then provide two novel algorithms solving this problem efficiently when $\mathcal{X}$ is a centered ellipsoid. Our findings provide the first known method to implement optimistic algorithms for linear bandits in high dimensions.

Raymond Zhang, Hedi Hadiji, Richard Combes

We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm, which must be at least $Ω(\min(d σ\sqrt{T} + d \|θ\|_{A}, \|θ\|_{A} T))$ where $d$ is the dimension, $T$ the time horizon, $σ^2$ the noise variance, $A$ a matrix defining the set of actions and $θ$ the vector of unknown parameters. We then provide an algorithm whose regret matches this bound to a multiplicative universal constant. The algorithm is non-classical in the sense that it is not optimistic, and it is not a sampling algorithm. The main idea is to combine a novel sequential procedure to estimate $\|θ\|$, followed by an explore-and-commit strategy informed by this estimate. The algorithm is highly computationally efficient, and a run requires only time $O(dT + d^2 \log(T/d) + d^3)$ and memory $O(d^2)$, in contrast with known optimistic algorithms, which are not implementable in polynomial time. We go beyond minimax optimality and show that our algorithm is locally asymptotically minimax optimal, a much stronger notion of optimality. We further provide numerical experiments to illustrate our theoretical findings.

Amir H. Ashouri, Muhammad Asif Manzoor, Duc Minh Vu et al. · utoronto

The key to performance optimization of a program is to decide correctly when a certain transformation should be applied by a compiler. This is an ideal opportunity to apply machine-learning models to speed up the tuning process; while this realization has been around since the late 90s, only recent advancements in ML enabled a practical application of ML to compilers as an end-to-end framework. This paper presents ACPO: An AI-Enabled Compiler Framework, a novel framework that provides LLVM with simple and comprehensive tools to benefit from employing ML models for different optimization passes. We first showcase the high-level view, class hierarchy, and functionalities of ACPO and subsequently, demonstrate \taco{a couple of use cases of ACPO by ML-enabling the Loop Unroll and Function Inlining passes used in LLVM's O3. and finally, describe how ACPO can be leveraged to optimize other passes. Experimental results reveal that the ACPO model for Loop Unroll can gain on average 4%, 3%, 5.4%, and 0.2% compared to LLVM's vanilla O3 optimization when deployed on Polybench, Coral-2, CoreMark, and Graph-500, respectively. Furthermore, by including both Function Inlining and Loop Unroll models, ACPO can provide a combined speedup of 4.5% on Polybench and 2.4% on Cbench when compared with LLVM's O3, respectively.

Alvaro Cabrejas-Egea, Raymond Zhang, Neil Walton

Recently, Intelligent Transportation Systems are leveraging the power of increased sensory coverage and computing power to deliver data-intensive solutions achieving higher levels of performance than traditional systems. Within Traffic Signal Control (TSC), this has allowed the emergence of Machine Learning (ML) based systems. Among this group, Reinforcement Learning (RL) approaches have performed particularly well. Given the lack of industry standards in ML for TSC, literature exploring RL often lacks comparison against commercially available systems and straightforward formulations of how the agents operate. Here we attempt to bridge that gap. We propose three different architectures for TSC RL agents and compare them against the currently used commercial systems MOVA, SurTrac and Cyclic controllers and provide pseudo-code for them. The agents use variations of Deep Q-Learning and Actor Critic, using states and rewards based on queue lengths. Their performance is compared in across different map scenarios with variable demand, assessing them in terms of the global delay and average queue length. We find that the RL-based systems can significantly and consistently achieve lower delays when compared with existing commercial systems.

Raymond Zhang, Richard Combes

In this paper we consider Thompson Sampling (TS) for combinatorial semi-bandits. We demonstrate that, perhaps surprisingly, TS is sub-optimal for this problem in the sense that its regret scales exponentially in the ambient dimension, and its minimax regret scales almost linearly. This phenomenon occurs under a wide variety of assumptions including both non-linear and linear reward functions, with Bernoulli distributed rewards and uniform priors. We also show that including a fixed amount of forced exploration to TS does not alleviate the problem. We complement our theoretical results with numerical results and show that in practice TS indeed can perform very poorly in some high dimensional situations.