We consider the problem of sequential prediction of an $m$-ary sequence, where at each epoch, (i) the environment selects an outcome from an $m$-ary alphabet, (ii) the learner selects a probability distribution over the same alphabet (unaware of the outcome generated by the environment), and finally, (iii) the learner incurs a cost that depends on the probability assigned to the outcome. The cost function we consider captures the complexity of predicting the outcome generated by the environment, in a scenario where the aforementioned prediction is performed via comparative queries to a lying oracle. We consider both stochastic and adversarial environments, propose algorithms for both settings, and establish logarithmic upper bounds on their regret.
Detection models running in adversarial environments face a malicious distribution that drifts rapidly while the benign distribution stays comparatively stable, so teams retrain and redeploy constantly to stay ahead of new threats. Retraining tends to change the output prediction scores, which breaks downstream users of the model. For these security-oriented models we need consistent false-positive rate (FPR) across all output values, whereas standard probability-calibration methods target class probability rather than an FPR contract. We introduce a method built on top of existing calibration primitives that targets the whole FPR curve, giving scores a consistent FPR meaning across deployments. On one held-out split, the observed relative FPR error was at most 2.3% from 10% down to 0.1% FPR and 7.2% at 0.01% FPR. The shipped artifact remains under 200 KB in measurements across calibration sets from 1K to 10M benign samples.
Deep research agents have demonstrated remarkable capabilities in autonomous information gathering and synthesis, yet their training remains constrained by the static nature of simulated environments, the limits of fact-retrieval-only task designs, and the inefficiency of outcome-based reinforcement learning. In this work, we propose MetaResearcher, a novel framework that scales deep research agent training across four synergistic dimensions. First, we introduce an Evolving Virtual World that injects temporal dynamics and adversarial misinformation into the training environment, forcing agents to develop source credibility assessment and temporal conflict resolution skills. Second, we design Discovery-Oriented Tasks -- including hypothesis generation and contradiction resolution -- that transcend simple fact retrieval and push agents toward genuine research behaviors. Third, we propose a Self-Reflective Meta-Reward mechanism within the GRPO framework that jointly optimizes for answer correctness, search path efficiency, reflection depth, and tool call diversity, directly addressing the repetitive action loop problem observed in prior work. Fourth, we introduce a Heterogeneous Multi-Agent Swarm architecture comprising specialized Scout, Filter, and Synthesizer models that learn collaborative research strategies through coordinated reinforcement learning. Built upon the LiteResearcher infrastructure, MetaResearcher requires zero marginal API cost for training while targeting substantial improvements in both benchmark performance (GAIA, Xbench-DS) and epistemic robustness under adversarial conditions. We present the complete framework design, training methodology, and planned experimental validation.