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We propose the first adversarially robust algorithm for monotone submodular maximization under single and multiple knapsack constraints with scalable implementations in distributed and streaming settings. For a single knapsack constraint,…
Recent advancements in large language model alignment leverage token-level supervisions to perform fine-grained preference optimization. However, existing token-level alignment methods either optimize on all available tokens, which can be…
Combinatorial optimization problems are one of the target applications of current quantum technology, mainly because of their industrial relevance, the difficulty of solving large instances of them classically, and their equivalence to…
We consider solving a combinatorial optimization problem with unknown knapsack constraints using a membership oracle for each unknown constraint such that, given a solution, the oracle determines whether the constraint is satisfied or not…
In this paper we enhance Generalized Self-Adapting Particle Swarm Optimization algorithm (GAPSO), initially introduced at the Parallel Problem Solving from Nature 2018 conference, and to investigate its properties. The research on GAPSO is…
In practise, it is often desirable to provide the decision-maker with a rich set of diverse solutions of decent quality instead of just a single solution. In this paper we study evolutionary diversity optimization for the knapsack problem…
Semidefinite programming (SDP) is a powerful tool for tackling a wide range of computationally hard problems such as clustering. Despite the high accuracy, semidefinite programs are often too slow in practice with poor scalability on large…
Online and offline RLHF methods, such as PPO and DPO, have been highly successful in aligning AI with human preferences. Despite their success, however, these methods suffer from fundamental limitations: (a) Models trained with RLHF can…
In this paper, we consider a multi-stage dynamic assortment optimization problem with multi-nomial choice modeling (MNL) under resource knapsack constraints. Given the current resource inventory levels, the retailer makes an assortment…
We provide an exact algorithm to solve the log-linear continuous (fractional) knapsack problem. The algorithm is based on two lemmas that follow from the application of weak duality theorem and complementary slackness theorem to the linear…
Text document clustering can play a vital role in organizing and handling the everincreasing number of text documents. Uninformative and redundant features included in large text documents reduce the effectiveness of the clustering…
This paper targets to a novel but practical recommendation problem named exact-K recommendation. It is different from traditional top-K recommendation, as it focuses more on (constrained) combinatorial optimization which will optimize to…
Knapsack problems are classic models that can formulate a wide range of applications. In this work, we deal with the Budgeted Maximum Coverage Problem (BMCP), which is a generalized 0-1 knapsack problem. Given a set of items with…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
Topology optimization by optimally distributing materials in a given domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would…
Direct Preference Optimisation (DPO) is effective at significantly improving the performance of large language models (LLMs) on downstream tasks such as reasoning, summarisation, and alignment. Using pairs of preferred and dispreferred…
This paper presents a novel approach to solving the Flying Sidekick Travelling Salesman Problem (FSTSP) using a state-of-the-art self-adaptive genetic algorithm. The Flying Sidekick Travelling Salesman Problem is a combinatorial…
Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…
We present an $n\Delta^{O(k^2)}$ time algorithm to obtain an optimal solution for $1$-dimensional cutting stock problem: the bin packing problem of packing $n$ items onto unit capacity bins under the restriction that the number of item…
The Simple Plant Location Problem with Order (SPLPO) is a variant of the Simple Plant Location Problem (SPLP), where the customers have preferences over the facilities which will serve them. In particular, customers define their preferences…