inventory management teams

Abstract: In the online unweighted knapsack problem, items arrive sequentially and must be accepted or rejected immediately for a bounded-capacity knapsack, aiming to maximize the total size of accepted items. When decisions are irrevocable, no algorithm achieves a non-trivial competitive ratio. An essential relaxation that circumvents this impossibility is to allow previously accepted items to be removed from the knapsack (a.k.a. removal). In this work, we investigate possible further improvements on the competitive ratio with removal by bringing together two other previously proposed model extensions: knowledge of an upper bound on the item sizes (a.k.a. bound awareness) and ability to reinsert previously rejected items(a.k.a.recourse). Our contributions are twofold. First, we establish close upper and lower bounds on the competitive ratio under bound awareness, removal and recourse. We show that significant improvements on the best known competitive ratio are possible when the upper bound on the item sizes is not too restrictive and only few uses of recourse are available. Second, we introduce the notion of adaptive online algorithms which do not require to know any upper bound on the item sizes but still achieve performance guarantees comparable to the ones obtained under the bound awareness model.

Abstract: We study sparse linear contextual bandits with knapsack constraints under joint reward and consumption corruption. Consumption corruption creates a challenge beyond corrupted rewards: it affects not only statistical estimates, but also the recorded budget, resource prices, and stopping decisions that govern future allocation. We develop Robust Optimistic Primal--Dual (ROPD), an estimator-modular framework that combines corruption-aware confidence widths with online resource prices and a budget-safety rule. With concrete sparse implementation, ROPD achieves regret against a clean population-LP benchmark of $\widetilde O(T^{2/3}+ΓT^{1/3})$ under forced exploration and population-design coverage, and $\widetilde O(\sqrt T+Γ)$ under on-policy realized-design coverage, for a supplied valid corruption bound $Γ$ under the stated proportional-budget scaling and fixed model/design parameters. When the corruption level is unknown, Shared-Grid adapts confidence radii around common point estimates fitted to a single realized history, incurring explicit initialization and master-comparison costs; its sharper on-policy guarantee additionally requires recommendation coverage. Both methods preserve observed budgets on every realization and bound clean resource violation by cumulative consumption corruption. These results connect corruption-robust sparse estimation with resource accounting, pricing, and stopping in high-dimensional online allocation.

Abstract: We introduce loss-conditioned state execution, a model-agnostic method that decides whether to execute a world model's fixed feasible proposal or retain the current state. Predictive informativeness alone, however, does not establish whether an update will reduce downstream loss. Occurrence ranking can approach perfection while persistence remains the unique absolute-loss Bayes action. Two transition laws can also share occurrence information and conditional variance yet require opposite absolute-loss decisions. We formalize state movability as the existence of a loss-reducing feasible correction and distinguish it from the benefit of a particular proposal. Our method constructs a loss-specific feasible proposal from a predictive distribution and evaluates its groupwise bounded-loss gain over persistence on independent calibration units. The proposal is executed only in groups with a positive simultaneous lower confidence bound. For fixed proposals and groups with bounded unit losses, we prove that every accepted group has lower expected loss than persistence with high probability when calibration units are i.i.d. draws from the target population. Experiments on public forecasting and action-conditioned dynamics benchmarks show supported updates and a trade-off between certification and coverage. On 28,684 held-out M4 Monthly series, the method executes the proposal for 14.0% of series and achieves bounded loss 0.588, compared with 0.599 for persistence and 0.621 for always executing the proposal. The paired 95% bootstrap intervals for both comparisons lie below zero. In constrained forecasting of six unhealthy-inventory types from JD$\mbox{.}$com, a leading e-retailer in China, strong occurrence-ranking signal coexists with a loss-based preference for persistence, illustrating why event predictability and state execution must be evaluated separately.