Alireza Bakhtiari

Shuai Liu, Alireza Bakhtiari, Alex Ayoub et al.

We study stochastic contextual logistic bandits under the simple regret objective. While simple regret guarantees have been established for the linear case, no such results were previously known for the logistic setting. Building on ideas from contextual linear bandits and self-concordant analysis, we propose the first algorithm that achieves simple regret $\tilde{\mathcal{O}}(d/\sqrt{T})$. Notably, the leading term of our regret bound is free of the constant $κ= \mathcal O(\exp(S))$, where $S$ is a bound on the magnitude of the unknown parameter vector. The algorithm is shown to be fully tractable when the action set is finite. We also introduce a new variant of Thompson Sampling tailored to the simple-regret setting. This yields the first simple regret guarantee for randomized algorithms in stochastic contextual linear bandits, with regret $\tilde{\mathcal{O}}(d^{3/2}/\sqrt{T})$. Extending this method to the logistic case, we obtain a similarly structured Thompson Sampling algorithm that achieves the same regret bound -- $\tilde{\mathcal{O}}(d^{3/2}/\sqrt{T})$ -- again with no dependence on $κ$ in the leading term. The randomized algorithms, as expected, are cheaper to run than their deterministic counterparts. Finally, we conducted a series of experiments to empirically validate these theoretical guarantees.

Alireza Bakhtiari, Alex Ayoub, Samuel Robertson et al.

We establish a lower bound on the eluder dimension of generalised linear model classes, showing that standard eluder dimension-based analysis cannot lead to first-order regret bounds. To address this, we introduce a localisation method for the eluder dimension; our analysis immediately recovers and improves on classic results for Bernoulli bandits, and allows for the first genuine first-order bounds for finite-horizon reinforcement learning tasks with bounded cumulative returns.

Alex Ayoub, David Szepesvári, Alireza Bakhtiari et al.

This paper investigates the impact of the loss function in value-based methods for reinforcement learning through an analysis of underlying prediction objectives. We theoretically show that mean absolute error is a better prediction objective than the traditional mean squared error for controlling the learned policy's suboptimality gap. Furthermore, we present results that different loss functions are better aligned with these different regression objectives: binary and categorical cross-entropy losses with the mean absolute error and squared loss with the mean squared error. We then provide empirical evidence that algorithms minimizing these cross-entropy losses can outperform those based on the squared loss in linear reinforcement learning.