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Publications
Planning and Learning in Risk-Aware Restless Multi-Arm Bandits
In restless multi-arm bandits, a central agent is tasked with optimally distributing limited resources across several bandits (arms), with e… (see more)ach arm being a Markov decision process. In this work, we generalize the traditional restless multi-arm bandit problem with a risk-neutral objective by incorporating risk-awareness. We establish indexability conditions for the case of a risk-aware objective and provide a solution based on Whittle index. In addition, we address the learning problem when the true transition probabilities are unknown by proposing a Thompson sampling approach and show that it achieves bounded regret that scales sublinearly with the number of episodes and quadratically with the number of arms. The efficacy of our method in reducing risk exposure in restless multi-arm bandits is illustrated through a set of numerical experiments in the contexts of machine replacement and patient scheduling applications under both planning and learning setups.
Current backdoor defense methods are evaluated against a single attack at a time. This is unrealistic, as powerful machine learning systems … (see more)are trained on large datasets scraped from the internet, which may be attacked multiple times by one or more attackers. We demonstrate that multiple backdoors can be simultaneously installed in a single model through parallel data poisoning attacks without substantially degrading clean accuracy. Furthermore, we show that existing backdoor defense methods do not effectively defend against multiple simultaneous attacks. Finally, we leverage insights into the nature of backdoor attacks to develop a new defense, BaDLoss (**Ba**ckdoor **D**etection via **Loss** Dynamics), that is effective in the multi-attack setting. With minimal clean accuracy degradation, BaDLoss attains an average attack success rate in the multi-attack setting of 7.98% in CIFAR-10, 10.29% in GTSRB, and 19.17% in Imagenette, compared to the average of other defenses at 63.44%, 74.83%, and 41.74% respectively. BaDLoss scales to ImageNet-1k, reducing the average attack success rate from 88.57% to 15.61%.
Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof sys… (see more)tem. However, the space of possible tactics is vast and complex, while the available training data for formal proofs is limited, posing a significant challenge to LLM-based tactic generation. To address this, we introduce a neuro-symbolic tactic generator that synergizes the mathematical intuition learned by LLMs with domain-specific insights encoded by symbolic methods. The key aspect of this integration is identifying which parts of mathematical reasoning are best suited to LLMs and which to symbolic methods. While the high-level idea of neuro-symbolic integration is broadly applicable to various mathematical problems, in this paper, we focus specifically on Olympiad inequalities (Figure~1). We analyze how humans solve these problems and distill the techniques into two types of tactics: (1) scaling, handled by symbolic methods, and (2) rewriting, handled by LLMs. In addition, we combine symbolic tools with LLMs to prune and rank the proof goals for efficient proof search. We evaluate our framework on 161 challenging inequalities from multiple mathematics competitions, achieving state-of-the-art performance and significantly outperforming existing LLM and symbolic approaches without requiring additional training data.
In Markov decision processes (MDPs), quantile risk measures such as Value-at-Risk are a standard metric for modeling RL agents' preferences … (see more)for certain outcomes. This paper proposes a new Q-learning algorithm for quantile optimization in MDPs with strong convergence and performance guarantees. The algorithm leverages a new, simple dynamic program (DP) decomposition for quantile MDPs. Compared with prior work, our DP decomposition requires neither known transition probabilities nor solving complex saddle point equations and serves as a suitable foundation for other model-free RL algorithms. Our numerical results in tabular domains show that our Q-learning algorithm converges to its DP variant and outperforms earlier algorithms.
Data augmentation is a widely used and effective technique to improve the generalization performance of deep neural networks. Yet, despite o… (see more)ften facing limited data availability when working with medical images, it is frequently underutilized. This appears to come from a gap in our collective understanding of the efficacy of different augmentation techniques across different tasks and modalities. One modality where this is especially true is ultrasound imaging. This work addresses this gap by analyzing the effectiveness of different augmentation techniques at improving model performance across a wide range of ultrasound image analysis tasks. To achieve this, we introduce a new standardized benchmark of 14 ultrasound image classification and semantic segmentation tasks from 10 different sources and covering 11 body regions. Our results demonstrate that many of the augmentations commonly used for tasks on natural images are also effective on ultrasound images, even more so than augmentations developed specifically for ultrasound images in some cases. We also show that diverse augmentation using TrivialAugment, which is widely used for natural images, is also effective for ultrasound images. Moreover, our proposed methodology represents a structured approach for assessing various data augmentations that can be applied to other contexts and modalities.
Data augmentation is a widely used and effective technique to improve the generalization performance of deep neural networks. Yet, despite o… (see more)ften facing limited data availability when working with medical images, it is frequently underutilized. This appears to come from a gap in our collective understanding of the efficacy of different augmentation techniques across different tasks and modalities. One modality where this is especially true is ultrasound imaging. This work addresses this gap by analyzing the effectiveness of different augmentation techniques at improving model performance across a wide range of ultrasound image analysis tasks. To achieve this, we introduce a new standardized benchmark of 14 ultrasound image classification and semantic segmentation tasks from 10 different sources and covering 11 body regions. Our results demonstrate that many of the augmentations commonly used for tasks on natural images are also effective on ultrasound images, even more so than augmentations developed specifically for ultrasound images in some cases. We also show that diverse augmentation using TrivialAugment, which is widely used for natural images, is also effective for ultrasound images. Moreover, our proposed methodology represents a structured approach for assessing various data augmentations that can be applied to other contexts and modalities.
Reinforcement learning algorithms typically necessitate extensive exploration of the state space to find optimal policies. However, in safet… (see more)y-critical applications, the risks associated with such exploration can lead to catastrophic consequences. Existing safe exploration methods attempt to mitigate this by imposing constraints, which often result in overly conservative behaviours and inefficient learning. Heavy penalties for early constraint violations can trap agents in local optima, deterring exploration of risky yet high-reward regions of the state space. To address this, we introduce a method that explicitly learns state-conditioned safety representations. By augmenting the state features with these safety representations, our approach naturally encourages safer exploration without being excessively cautious, resulting in more efficient and safer policy learning in safety-critical scenarios. Empirical evaluations across diverse environments show that our method significantly improves task performance while reducing constraint violations during training, underscoring its effectiveness in balancing exploration with safety.
Reinforcement learning algorithms typically necessitate extensive exploration of the state space to find optimal policies. However, in safet… (see more)y-critical applications, the risks associated with such exploration can lead to catastrophic consequences. Existing safe exploration methods attempt to mitigate this by imposing constraints, which often result in overly conservative behaviours and inefficient learning. Heavy penalties for early constraint violations can trap agents in local optima, deterring exploration of risky yet high-reward regions of the state space. To address this, we introduce a method that explicitly learns state-conditioned safety representations. By augmenting the state features with these safety representations, our approach naturally encourages safer exploration without being excessively cautious, resulting in more efficient and safer policy learning in safety-critical scenarios. Empirical evaluations across diverse environments show that our method significantly improves task performance while reducing constraint violations during training, underscoring its effectiveness in balancing exploration with safety.
The self-attention mechanism traditionally relies on the softmax operator, necessitating positional embeddings like RoPE, or position biases… (see more) to account for token order.
But current methods using still face length generalisation challenges.
We investigate an alternative attention mechanism based on the stick-breaking process in larger scale settings.
The method works as follows: For each token before the current, we determine a break point, which represents the proportion of the stick, the weight of the attention, to allocate to the current token.
We repeat this on the remaining stick, until all tokens are allocated a weight, resulting in a sequence of attention weights.
This process naturally incorporates recency bias, which has linguistic motivations for grammar parsing (Shen et al., 2017).
We study the implications of replacing the conventional softmax-based attention mechanism with stick-breaking attention.
We then discuss implementation of numerically stable stick-breaking attention and adapt Flash Attention to accommodate this mechanism.
When used as a drop-in replacement for current softmax+RoPE attention systems, we find that stick-breaking attention performs competitively with current methods on length generalisation and downstream tasks.
Stick-breaking also performs well at length generalisation, allowing a model trained with
When deploying machine learning models in the real world, we often face the challenge of “unlearning” specific data points or subsets a… (see more)fter training. Inspired by Domain-Adversarial Training of Neural Networks (DANN), we propose a novel algorithm,SURE, for targeted unlearning.SURE treats the process as a domain adaptation problem, where the “forget set” (data to be removed) and a validation set from the same distribution form two distinct domains. We train a domain classifier to discriminate between representations from the forget and validation sets.Using a gradient reversal strategy similar to DANN, we perform gradient updates to the representations to “fool” the domain classifier and thus obfuscate representations belonging to the forget set. Simultaneously, gradient descent is applied to the retain set (original training data minus the forget set) to preserve its classification performance. Unlike other unlearning approaches whose training objectives are built based on model outputs, SURE directly manipulates the representations.This is key to ensure robustness against a set of more powerful attacks than currently considered in the literature, that aim to detect which examples were unlearned through access to learned embeddings. Our thorough experiments reveal that SURE has a better unlearning quality to utility trade-off compared to other standard unlearning techniques for deep neural networks.
