We address differentially private stochastic bandit problems by leveraging Thompson Sampling with Gaussian priors and Gaussian differential privacy (GDP). We propose DP-TS-UCB, a novel parametrized private algorithm that enables trading off privacy and regret. DP-TS-UCB satisfies $ \tilde{O} \left(T^{0.25(1-\alpha)}\right)$-GDP and achieves $O \left(K\ln^{\alpha+1}(T)/\Delta \right)$ regret bounds, where $K$ is the number of arms, $ \Delta$ is the sub-optimality gap, $T$ is the learning horizon, and $\alpha \in [0,1]$ controls the trade-off between privacy and regret. Theoretically, DP-TS-UCB relies on anti-concentration bounds for the Gaussian distributions, linking the exploration mechanisms of Thompson Sampling and Upper Confidence Bound, which may be of independent research interest.

Concept Bottleneck Models (CBMs) propose to enhance the trustworthiness of AI systems by constraining their decisions on a set of human understandable concepts. However, CBMs typically rely on datasets with assumedly accurate concept labels—an assumption often violated in practice which we show can significantly degrade performance. To address this, we introduce the Concept Preference Optimization (CPO) objective, a new loss function based on Direct Preference Optimization, which effectively mitigates the negative impact of concept mislabeling on CBM performance. We provide an analysis on some key properties of the CPO objective showing it directly optimizes for the concept’s posterior distribution, and contrast it against Binary Cross Entropy (BCE) where we show CPO is inherently less sensitive to concept noise. We empirically confirm our analysis finding that CPO consistently outperforms BCE in three real-world datasets with and without added label noise

Despite its widespread adoption, Adam's advantage over Stochastic Gradient Descent (SGD) lacks a comprehensive theoretical explanation. This paper investigates Adam's sensitivity to rotations of the parameter space. We observe that Adam's performance in training transformers degrades under random rotations of the parameter space, indicating a crucial sensitivity to the choice of basis in practice. This reveals that conventional rotation-invariant assumptions are insufficient to capture Adam's advantages theoretically. To better understand the rotation-dependent properties that benefit Adam, we also identify structured rotations that preserve or even enhance its empirical performance. We then examine the rotation-dependent assumptions in the literature and find that they fall short in explaining Adam's behavior across various rotation types. In contrast, we verify the orthogonality of the update as a promising indicator of Adam’s basis sensitivity, suggesting it may be the key quantity for developing rotation-dependent theoretical frameworks that better explain its empirical success.

Constrained optimization offers a powerful framework to prescribe desired behaviors in neural network models. Typically, constrained problems are solved via their min-max Lagrangian formulations, which exhibit unstable oscillatory dynamics when optimized using gradient descent-ascent. The adoption of constrained optimization techniques in the machine learning community is currently limited by the lack of reliable, general-purpose update schemes for the Lagrange multipliers. This paper proposes the νPI algorithm and contributes an optimization perspective on Lagrange multiplier updates based on PI controllers, extending the work of Stooke, Achiam and Abbeel (2020). We provide theoretical and empirical insights explaining the inability of momentum methods to address the shortcomings of gradient descent-ascent, and contrast this with the empirical success of our proposed νPI controller. Moreover, we prove that νPI generalizes popular momentum methods for single-objective minimization. Our experiments demonstrate that νPI reliably stabilizes the multiplier dynamics and its hyperparameters enjoy robust and predictable behavior.

We propose two Thompson Sampling-like, model-based learning algorithms for episodic Markov decision processes (MDPs) with a finite time horizon. Our proposed algorithms are inspired by Optimistic Thompson Sampling (O-TS), empirically studied in Chapelle and Li [2011], May et al. [2012] for stochastic multi-armed bandits. The key idea for the original O-TS is to clip the posterior distribution in an optimistic way to ensure that the sampled models are always better than the empirical models. Both of our proposed algorithms are easy to implement and only need one posterior sample to construct an episode-dependent model. Our first algorithm, Optimistic Thompson Sampling for MDPs (O-TS-MDP), achieves a $\widetilde{O} \left(\sqrt{AS^2H^4T} \right)$ regret bound, where $S$ is the size of the state space, $A$ is the size of the action space, $H$ is the number of time-steps per episode and $T$ is the number of episodes. Our second algorithm, Optimistic Thompson Sampling plus for MDPs (O-TS-MDP$^+$), achieves the (near)-optimal $\widetilde{O} \left(\sqrt{ASH^3T} \right)$ regret bound by taking a more aggressive clipping strategy. Since O-TS was only empirically studied previously, we derive regret bounds of O-TS for stochastic bandits. In addition, we propose, O-TS-Bandit$^+$, a randomized version of UCB1 [Auer et al., 2002], for stochastic bandits. Both O-TS and O-TS-Bandit$^+$ achieve the optimal $O\left(\frac{A\ln(T)}{\Delta} \right)$ problem-dependent regret bound, where $\Delta$ denotes the sub-optimality gap.