A major challenge for stochastic optimization is the cost of updating model parameters especially when the number of parameters is large. Updating parameters frequently can prove to be computationally or monetarily expensive. In this paper, we introduce an efficient primal-dual based online algorithm that performs lazy updates to the parameter vector and show that its performance is competitive with reasonable strategies which have the benefit of hindsight. We demonstrate the effectiveness of our algorithm in the online portfolio selection domain where a trader has to pay proportional transaction costs every time his portfolio is updated. Our Online Lazy Updates (OLU) algorithm takes into account the transaction costs while computing an optimal portfolio which results in sparse updates to the portfolio vector. We successfully establish the robustness and scalability of our lazy portfolio selection algorithm with extensive theoretical and experimental results on two real-world datasets.
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