A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit

In this paper, we consider the contextual variant of the MNL-Bandit problem. More specifically, we consider a dynamic set optimization problem, where a decision-maker offers a subset (assortment) of products to a consumer and observes their response in every round. Consumers purchase products to maximize their utility. We assume that a set of attributes describes the products, and the mean utility of a product is linear in the values of these attributes. We model consumer choice behavior using the widely used Multinomial Logit (MNL) model and consider the decision maker problem of dynamically learning the model parameters while optimizing cumulative revenue over the selling horizon $T$. Though this problem has attracted considerable attention in recent times, many existing methods often involve solving an intractable non-convex optimization problem. Their theoretical performance guarantees depend on a problem-dependent parameter which could be prohibitively large. In particular, existing algorithms for this problem have regret bounded by $O(\sqrt{\kappa d T})$, where $\kappa$ is a problem-dependent constant that can have an exponential dependency on the number of attributes. In this paper, we propose an optimistic algorithm and show that the regret is bounded by $O(\sqrt{dT} + \kappa)$, significantly improving the performance over existing methods. Further, we propose a convex relaxation of the optimization step, which allows for tractable decision-making while retaining the favourable regret guarantee.Comment: updated version, under revie

The MNL-Bandit Problem: Theory and Applications

One fundamental problem in revenue management that arises in many settings including retail and display-based advertising is assortment planning. Here, the focus is on understanding how consumers select from a large number of substitutable items and identifying the optimal offer set to maximize revenues. Typically, for tractability, we assume a model that captures consumer preferences and focus on computing the optimal offer set. A significant challenge here is the lack of knowledge on consumer preferences. In this thesis, we consider the multinomial logit choice model, the most popular model for this application domain and develop tractable robust algorithms for assortment planning under uncertainty. We also quantify the fundamental performance limits from both computational and information theoretic perspectives for such problems. The existing methods for the dynamic problem follow ``estimate, then optimize'' paradigm, which require knowledge of certain parameters that are not readily available, thereby limiting their applicability in practice. We address this gap between theory and practice by developing new theoretical tools which will aid in designing algorithms that judiciously combine exploration and exploitation to maximize revenues. We first present an algorithm based on the principle of ``optimism under uncertainty'' that is simultaneously robust and adaptive to instance complexity. We then leverage this theory to develop a Thompson Sampling (TS) based framework with theoretical guarantees for the dynamic problem. This is primarily motivated by the growing popularity of TS approaches in practice due to their attractive empirical properties. We also indicate how to generalize the TS framework to design scalable dynamic learning algorithms for high-dimensional data and discuss empirical gains of such approaches from preliminary implementations on Flipkart, a large e-commerce firm in India

Recirculating Aquaculture System Conditioning

A newly established recirculating aquaculture system should be conditioned before stocking of the live animal into the RAS tanks for the culture. It is necessary because fishes produce waste from the day of stocking as a result of the nutrition they receive. It is not only the waste produced from the fish but also from the waste generated due to feed and feeding activity. These wastes, mainly ammonia and nitrite are very toxic to the fish and are an environmental stressor that causes reduced appetite, reduced growth rate and death at high concentrations. These toxic waste needs to be removed from the system from the date of stocking otherwise will create problem to the stocked animals. To remove these wastes, the biofilter or biological filter, which form a key component in the filtration system of a recirculating aquaculture system (RAS) needs to be activated. The biofilter houses the nitrifying bacteria and is the primary site where biological nitrification occurs. Nitrifying bacteria converts toxic nitrogenous waste produced or excreted by the aquatic organisms into the simpler form, which is less toxic to the fishes

Water quality requirements for Recirculatory Aquaculture Systems

Culture of marine finfishes in a controlled condition is an upcoming industry, which is very much essential to satisfy the rising demand for protein rich seafood. Traditional aquaculture ponds use huge quantity of water and land to produce lesser output. Whereas Recirculatory Aquaculture System (RAS) is one such system in which fishes are cultured in high density at controlled environmental condition with lesser usage of water and comparatively less area of land to produce higher output. RAS is designed to minimize or reduce dependence on water exchange and flushing in fish culture units. The systems have practical applications in commercial aquaculture hatcheries, holding tanks and aquaria systems as well as small scale aquaculture projects. Water is specifically recirculated, when there is a specific need to minimize water replacement, to maintain the quality condition which differ from the supply water or to compensate for an insufficient water supply

Recirculating Aquaculture System engineering: Design, components and construction

Most fish and crustacean aquaculture is undertaken in earthen ponds or large tanks with flowing water. Pond culture requires large areas of flat land and significant quantities of clean groundwater. Flow-through tank aquaculture requires less land but needs more water per kg of fish produced to maintain good growing conditions within the tank. Recirculating aquaculture systems re-use water over and over, cleaning the waste from the water and providing oxygen to the fish. Because water is reused, recirculating fish production systems utilize only a fraction of the water required by traditional fish production techniques. A small domestic well producing three to five gallons per minute, when coupled with the proper recirculating technology, can be used in the production of thousands of kilo of fish annually. There is no doubt that fish can be reared in large quantities and at high densities in recirculating systems. However, the economic viability of growing fish in recirculating systems is not ascertained. Before initiating the fish culture using recirculating technology, essential googleprinciples involved in the technology being used must be understood. In almost every successful application, highly technological solutions that have been evaluated are incorporated into the aquaculture systems