We revisit the finite-armed linear bandit model by Nelson et al. (2022), where contexts and rewards are governed by a finite hidden Markov chain. Nelson et al. (2022) approach this model by a reduction to linear contextual bandits; but to do so, they actually introduce a simplification in which rewards are linear functions of the posterior probabilities over the hidden states given the observed contexts, rather than functions of the hidden states themselves. Their analysis (but not their algorithm) also does not take into account the estimation of the HMM parameters, and only tackles expected, not high-probability, bounds, which suffer in addition from unnecessary complex dependencies on the model (like reward gaps). We instead study the more natural model incorporating direct dependencies in the hidden states (on top of dependencies on the observed contexts, as is natural for contextual bandits) and also obtain stronger, high-probability, regret bounds for a fully adaptive strategy that estimates HMM parameters online. These bounds do not depend on the reward functions and only depend on the model through the estimation of the HMM parameters.

Despite their dominance in vision and language, deep neural networks often underperform relative to tree-based models on tabular data. To bridge this gap, we incorporate five key inductive biases into deep learning: robustness to irrelevant features, axis alignment, localized irregularities, feature heterogeneity, and training stability. We propose \emph{LassoFlexNet}, an architecture that evaluates the linear and nonlinear marginal contribution of each input via Per-Feature Embeddings, and sparsely selects relevant variables using a Tied Group Lasso mechanism. Because these components introduce optimization challenges that destabilize standard proximal methods, we develop a \emph{Sequential Hierarchical Proximal Adaptive Gradient optimizer with exponential moving averages (EMA)} to ensure stable convergence. Across $52$ datasets from three benchmarks, LassoFlexNet matches or outperforms leading tree-based models, achieving up to a $10$\% relative gain, while maintaining Lasso-like interpretability. We substantiate these empirical results with ablation studies and theoretical proofs confirming the architecture's enhanced expressivity and structural breaking of undesired rotational invariance.

One of the most common machine learning setups is logistic regression. In many classification models, including neural networks, the final prediction is obtained by applying a logistic link function to a linear score. In binary logistic regression, the feedback can be either soft labels, corresponding to the true conditional probability of the data (as in distillation), or sampled hard labels (taking values $\pm 1$). We point out a fundamental problem that arises even in a particularly favorable setting, where the goal is to learn a noise-free soft target of the form $σ(\mathbf{x}^{\top}\mathbf{w}^{\star})$. In the over-constrained case (i.e. the number of samples $n$ exceeds the input dimension $d$) with examples $(\mathbf{x}_i,σ(\mathbf{x}_i^{\top}\mathbf{w}^{\star}))$, it is sufficient to recover $\mathbf{w}^{\star}$ and hence achieve the Bayes risk. However, we prove that when the examples are labeled by hard labels $y_i$ sampled from the same conditional distribution $σ(\mathbf{x}_i^{\top}\mathbf{w}^{\star})$ and $\mathbf{w}^{\star}$ is $s$-sparse, then rotation-invariant algorithms are provably suboptimal: they incur an excess risk $Ω\!\left(\frac{d-1}{n}\right)$, while there are simple non-rotation invariant algorithms with excess risk $O(\frac{s\log d}{n})$. The simplest rotation invariant algorithm is gradient descent on the logistic loss (with early stopping). A simple non-rotation-invariant algorithm for sparse targets that achieves the above upper bounds uses gradient descent on the weights $u_i,v_i$, where now the linear weight $w_i$ is reparameterized as $u_iv_i$.

Since offline RL does not require access to the environment, it can be applied to problems where interaction with environment is infeasible,e.g., when collecting new data is costly (trade or finance [Zhang et al., 2020]), risky (autonomous driving [Sallab et al., 2017]) or illegal / unethical (healthcare [Raghu etal.,2017]).

How to design efficient algorithms is a central problem for reinforcement learning (RL).

The Hessian of f(Z) can be viewed as an KN KN matrix by vectorizing the matrix Z. For deeper linear networks, it can be shown that flat saddle points exist at the origin, but there are no spurious local minima [34,37]. While most of these results based on the bottom-up approach explain optimization and generalization of certain types of deep neural networks, they provided limited insights into the practice of deep learning. In fact, our proof techniques are inspired by recent results on low-rank matrix recovery [77,80]. Some of the metrics are similar to those presented in [1]. Figure 7 depicts the learning curves in terms of both the training and test accuracy for all three optimization algorithms (i.e., SGD, Adam, and LBFGS).

The algorithm [62] consider Algorithm 2 for the stochastic generalized linear bandit problem. Assume thatθ is the true parameter of the reward model. Then we consider the lower bounds. For fj(A) = 12(ej1eTj2 +ej2eTj1),A with j1 j2, fj(Ai) is only 1 wheni = j and 0 otherwise. With Claim D.12 and Claim D.11 we get that g C q To get 1), we writeVl = [v1, vl] Rd l and V l = [vl+1, vk].

Wewill also writeζθ(x) = fθ(x) f?(x)to denote the fitting error. We use Gaussian initialization: if` {1,2,...,L}, the weights are initialized as

Weshowthat when trained from scratch,thetraining process can be split into an initial sample-intensive stage where the correlation is boosted from zero to a nontrivial value, followed by a more sample-efficient stageoffurther improvement. Additionally,weprovethat, provided anontrivial correlation between the downstream and pretraining tasks, finetuning from a pretrained model allowsustobypass the initial sample-intensivestage.

In this section, we show a separation on the power of data-oblivious and data-aware poisoning attacks on classification. A different goal could be to make θ fail on a particular test set of adversary's interest, making it a targeted poisoning [3, 56] or increase the probability of a general "bad predicate" of θ [44]. We now state and prove our separation on the power of data-oblivious and data-aware poisoning attacks on classification. In particular we show that empirical risk minimization (ERM) algorithm could be much more susceptible to data-aware poisoning adversaries, compared to data-oblivious adversaries. On the other hand, any adversary will have much smaller advantage in the data-oblivious game.