  Ranking systems are the key components of modern Information Retrieval (IR)
applications, such as search engines and recommender systems. Besides the
ranking relevance to users, the exposure fairness to item providers has also
been considered an important factor in ranking optimization. Many fair ranking
algorithms have been proposed to jointly optimize both ranking relevance and
fairness. However, we find that most existing fair ranking methods adopt greedy
algorithms that only optimize rankings for the next immediate session or
request. As shown in this paper, such a myopic paradigm could limit the upper
bound of ranking optimization and lead to suboptimal performance in the long
term.
  To this end, we propose \textbf{FARA}, a novel \textbf{F}uture-\textbf{A}ware
\textbf{R}anking \textbf{A}lgorithm for ranking relevance and fairness
optimization. Instead of greedily optimizing rankings for the next immediate
session, FARA plans ahead by jointly optimizing multiple ranklists together and
saving them for future sessions. Specifically, FARA first uses the Taylor
expansion to investigate how future ranklists will influence the overall
fairness of the system. Then, based on the analysis of the Taylor expansion,
FARA adopts a two-phase optimization algorithm where we first solve an optimal
future exposure planning problem and then construct the optimal ranklists
according to the optimal future exposure planning. Theoretically, we show that
FARA is optimal for ranking relevance and fairness joint optimization.
Empirically, our extensive experiments on three semi-synthesized datasets show
that FARA is efficient, effective, and can deliver significantly better ranking
performance compared to state-of-the-art fair ranking methods. We make our
implementation public at
\href{https://github.com/Taosheng-ty/QP_fairness/}{https://github.com/Taosheng-ty/QP\_fairness/}.
