We study the distribution of regret in stochastic multi-armed bandits and episodic reinforcement learning through a unified framework. We formalize a distributional regret bound as a probabilistic guarantee that holds uniformly over all confidence levels $δ\in (0,1]$, thereby characterizing the regret distribution across the full range of $δ$. We present a simple UCBVI-style algorithm with exploration bonus $\min\{c_{1,k}/N, c_{2,k}/\sqrt{N}\}$, where $N$ denotes the visit count and $(c_{1,k},c_{2,k})$ are user-specified parameters. For arbitrary parameter sequences, we derive general gap-independent and gap-dependent distributional regret bounds, yielding a principled characterization of how the parameters control the trade-off between expected performance, tail risk, and instance-dependent behavior. In particular, our bounds achieve optimal trade-offs between expected and distributional regret in both minimax and instance-dependent regimes. As a special case, for multi-armed bandits with $A$ arms and horizon $T$, we obtain a distributional regret bound of order $\mathcal{O}(\sqrt{AT}\log(1/δ))$, confirming the conjecture of Lattimore & Szepesvári (2020, Section 17.1) for the first time.

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There is a growing demand for efficient data removal to comply with regulations like the GDPR and to mitigate the influence of biased or corrupted data. This has motivated the field of machine unlearning, which aims to eliminate the influence of specific data subsets without the cost of full retraining. In this work, we propose a statistical framework for machine unlearning with generic loss functions and establish theoretical guarantees. For squared loss, especially, we develop Unlearning Least Squares (ULS) and establish its minimax optimality for estimating the model parameter of remaining data when only the pre-trained estimator, forget samples, and a small subsample of the remaining data are available. Our results reveal that the estimation error decomposes into an oracle term and an unlearning cost determined by the forget proportion and the forget model bias. We further establish asymptotically valid inference procedures without requiring full retraining. Numerical experiments and real-data applications demonstrate that the proposed method achieves performance close to retraining while requiring substantially less data access.

Practical applications of machine learning often involve successive training iterations with changes to features and training examples. Ideally, changes in the output of any new model should only be improvements (wins) over the previous iteration, but in practice the predictions may change neutrally for many examples, resulting in extra net-zero wins and losses, referred to as unnecessary churn. These changes in the predictions are problematic for usability for some applications, and make it harder and more expensive to measure if a change is statistically significant positive. In this paper, we formulate the problem and present a stabilization operator to regularize a classifier towards a previous classifier. We use a Markov chain Monte Carlo stabilization operator to produce a model with more consistent predictions without adversely affecting accuracy. We investigate the properties of the proposal with theoretical analysis. Experiments on benchmark datasets for different classification algorithms demonstrate the method and the resulting reduction in churn.

This would be particularly useful for large datasets like imagenet. Table 2 shows the area under accuracydrop curve(AUC) on MNIST Figure 4for gradient when training traditionally,training using saliencyguided procedure andfine-tuning (smaller AUCindicates better performance).

Scale-invariance in games has recently emerged as a widely valued desirable property. Yet, almost all fast convergence guarantees in learning in games require prior knowledge of the utility scale. To address this, we develop learning dynamics that achieve fast convergence while being both scale-free, requiring no prior information about utilities, and scale-invariant, remaining unchanged under positive rescaling of utilities. For two-player zero-sum games, we obtain scale-free and scale-invariant dynamics with external regret bounded by $\tilde{O}(A_{\mathrm{diff}})$, where $A_{\mathrm{diff}}$ is the payoff range, which implies an $\tilde{O}(A_{\mathrm{diff}} / T)$ convergence rate to Nash equilibrium after $T$ rounds. For multiplayer general-sum games with $n$ players and $m$ actions, we obtain scale-free and scale-invariant dynamics with swap regret bounded by $O(U_{\mathrm{max}} \log T)$, where $U_{\mathrm{max}}$ is the range of the utilities, ignoring the dependence on the number of players and actions. This yields an $O(U_{\mathrm{max}} \log T / T)$ convergence rate to correlated equilibrium. Our learning dynamics are based on optimistic follow-the-regularized-leader with an adaptive learning rate that incorporates the squared path length of the opponents' gradient vectors, together with a new stopping-time analysis that exploits negative terms in regret bounds without scale-dependent tuning. For general-sum games, scale-free learning is enabled also by a technique called doubling clipping, which clips observed gradients based on past observations.

Despite advances in AI alignment, large language models (LLMs) remain vulnerable to adversarial attacks or jailbreaking, in which adversaries can modify prompts to induce unwanted behavior.

Asaconsequence, removing theerror P would reduce theloss more than removing the error N. Moreover, it is clear that this difference in error weighing increases withthelevelofimbalance between theclasses.