Mohammad Shahverdikondori

Fateme Jamshidi, Mohammad Shahverdikondori, Negar Kiyavash

We study multi-armed bandits under network interference, where each unit's reward depends on its own treatment and those of its neighbors in a given graph. This induces an exponentially large action space, making standard approaches computationally impractical. We propose a novel algorithm that uses the local graph structure to minimize regret. We derive a graph-dependent upper bound on cumulative regret that improves over prior work. Additionally, we provide the first lower bounds for bandits with arbitrary network interference, where each bound involves a distinct structural property of the graph. These bounds show that for both dense and sparse graphs, our algorithm is nearly optimal, with matching upper and lower bounds up to logarithmic factors. When the interference graph is unknown, a variant of our algorithm is Pareto optimal: no algorithm can uniformly outperform it across all instances. We complement our theoretical results with numerical experiments, showing that our approach outperforms the baseline methods.

Mohammad Shahverdikondori, Amir Mohammad Abouei, Alireza Rezaeimoghadam et al.

We introduce the problem of best arm identification (BAI) with post-action context, a new BAI problem in a stochastic multi-armed bandit environment and the fixed-confidence setting. The problem addresses the scenarios in which the learner receives a $\textit{post-action context}$ in addition to the reward after playing each action. This post-action context provides additional information that can significantly facilitate the decision process. We analyze two different types of the post-action context: (i) $\textit{non-separator}$, where the reward depends on both the action and the context, and (ii) $\textit{separator}$, where the reward depends solely on the context. For both cases, we derive instance-dependent lower bounds on the sample complexity and propose algorithms that asymptotically achieve the optimal sample complexity. For the non-separator setting, we do so by demonstrating that the Track-and-Stop algorithm can be extended to this setting. For the separator setting, we propose a novel sampling rule called $\textit{G-tracking}$, which uses the geometry of the context space to directly track the contexts rather than the actions. Finally, our empirical results showcase the advantage of our approaches compared to the state of the art.

Mohammad Shahverdikondori, Ehsan Mokhtarian, Negar Kiyavash

Causal discovery is essential for understanding relationships among variables of interest in many scientific domains. In this paper, we focus on permutation-based methods for learning causal graphs in Linear Gaussian Acyclic Models (LiGAMs), where the permutation encodes a causal ordering of the variables. Existing methods in this setting are not scalable due to their high computational complexity. These methods are comprised of two main components: (i) constructing a specific DAG, $\mathcal{G}^π$, for a given permutation $π$, which represents the best structure that can be learned from the available data while adhering to $π$, and (ii) searching over the space of permutations (i.e., causal orders) to minimize the number of edges in $\mathcal{G}^π$. We introduce QWO, a novel approach that significantly enhances the efficiency of computing $\mathcal{G}^π$ for a given permutation $π$. QWO has a speed-up of $O(n^2)$ ($n$ is the number of variables) compared to the state-of-the-art BIC-based method, making it highly scalable. We show that our method is theoretically sound and can be integrated into existing search strategies such as GRASP and hill-climbing-based methods to improve their performance.

Ahmed Sayeed Faruk, Mohammad Shahverdikondori, Elena Zheleva

In networked environments, users frequently share recommendations about content, products, services, and courses of action with others. The extent to which such recommendations are successful and adopted is highly contextual, dependent on the characteristics of the sender, recipient, their relationship, the recommended item, and the medium, which makes peer influence probabilities highly heterogeneous. Accurate estimation of these probabilities is key to understanding information diffusion processes and to improving the effectiveness of viral marketing strategies. However, learning these probabilities from data is challenging; static data may capture correlations between peer recommendations and peer actions but fails to reveal influence relationships. Online learning algorithms can learn these probabilities from interventions but either waste resources by learning from random exploration or optimize for rewards, thus favoring exploration of the space with higher influence probabilities. In this work, we study learning peer influence probabilities under a contextual linear bandit framework. We show that a fundamental trade-off can arise between regret minimization and estimation error, characterize all achievable rate pairs, and propose an uncertainty-guided exploration algorithm that, by tuning a parameter, attains any pair within this trade-off. Our experiments on semi-synthetic network datasets show the advantages of our method over static methods and contextual bandits that ignore this trade-off.

Mohammad Shahverdikondori, Jalal Etesami, Negar Kiyavash

We study regret minimization in causal bandits under causal sufficiency where the underlying causal structure is not known to the agent. Previous work has focused on identifying the reward's parents and then applying classic bandit methods to them, or jointly learning the parents while minimizing regret. We investigate whether such strategies are optimal. Somewhat counterintuitively, our results show that learning the parent set is suboptimal. We do so by proving that there exist instances where regret minimization and parent identification are fundamentally conflicting objectives. We further analyze both the known and unknown parent set size regimes, establish novel regret lower bounds that capture the combinatorial structure of the action space. Building on these insights, we propose nearly optimal algorithms that bypass graph and parent recovery, demonstrating that parent identification is indeed unnecessary for regret minimization. Experiments confirm that there exists a large performance gap between our method and existing baselines in various environments.