We study Bulow-Klemperer-style competition complexity in two-sided double auctions with $m$ unit-demand buyers drawn i.i.d. from $F_B$ and $n$ unit-supply sellers drawn i.i.d. from $F_S$. When $m \ge n$ and buyer valuations first-order stochastically dominate seller costs ($F_B \succeq_{\mathrm{FSD}} F_S$), we prove th...
Yang Cai, Vineet Gupta, Yan-Chen Jiang et al.· 1 citation
Autobidding has become a dominant paradigm in online advertising by enabling advertisers to set high-level goals while algorithms handle real-time bid optimization. A prominent example is the Return-on-Spend (RoS) value maximizer, which maximizes total value subject to an aggregate value-per-spend constraint. While mos...
Yang Cai, Christopher Liaw, Aranyak Mehta et al.· 0 citations
Auto-bidding is now widely adopted in online advertising platforms, allowing advertisers to specify high-level campaign objectives--such as maximizing total value subject to a return-on-spend (ROS) constraint--rather than manual per-query bids. A central question in algorithmic mechanism design is characterizing the wo...
Yang Cai, Vineet Gupta, Yan-Chen Jiang et al.· 1 citation
We present Cogentic, a multi-agent harness for automated proof discovery on open research problems. While frontier language models can generate strong mathematical ideas in a single shot, single-shot generation is often insufficient for open problems that require exploring multiple competing conjectures, overcoming sub...
Yang Cai, Vineet Gupta, Yan-Chen Jiang et al.· 0 citations
An algorithm is given, requiring no knowledge of the horizon, whose cumulative regret satisfies R_t, whose cumulative regret satisfies 1 + O(\sqrt{\ln \ln n / \ln n})\bigr)\sqrt{t \ln n / 2}$ simultaneously for every $t \ge 1$.
Yang Cai, Vineet Gupta, Yan-Chen Jiang et al.· 2 citations
This work builds on the variable-metric framework of Sakaue et al., adding a self-normalized rank-one update, and replaces the $\log\det$ potential by the trace power $\tr(H^{-1/2})$, which is bounded outright and removes the $\ln T$.
Yang Cai, Anupam Gupta, Vineet Gupta et al.· 3 citations· ⚡1
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