Although AI‑driven molecular generation has made breakthroughs, most current discovery pipelines remain in silico and wet‑lab feedback is limited to final validation, lacking an iterative loop. This work uses protein‑binding aptamer design as a low‑cost ($1‑$3 per candidate), short‑cycle (1‑2 weeks) sandbox to build a closed‑loop wet‑lab environment for AI systems.\ \ Agentic pipelines based on large language models were tasked with developing aptamer binders against α‑thrombin and myoglobin across three design‑test‑improve cycles, handling roughly 1,000 candidates per round and about 4,400 constructs in total. Statistically, bead‑corrected on‑target hit rates for new candidates rose on α‑thrombin from 0.0% in round 1 to 26.0% in round 2 and 42.1% in round 3 (37.1% when literature‑derived motifs are excluded), and on myoglobin from 10.2% to 3.7% and 33.5% respectively.\ \ Single‑clone bead‑binding titrations of eight full‑length α‑thrombin candidates showed strong concordance with pooled sequencing enrichment (Pearson $r = 0.90$). In these assays, literature‑derived motifs engineered by the agents achieved apparent affinities of $K_D = 24.6\sim133$ nM, while de‑novo scaffolds displayed low‑micromolar binding ($K_D \approx 1\ \mu$M).\ \ Using myoglobin binding data, the pipelines explored the G‑quadruplex binder space, diagnosed a drop in on‑target specificity from 75.0% to 19.1% due to cross‑reactivity, and recovered specificity to 72.4% through targeted strategies.\ \ The results demonstrate that empirical lab data outweigh existing computational proxies; iterative experimental feedback enables AI agents to detect assay artifacts and refine molecular designs across rounds.\ \ Review: This study proves that, within a cheap and rapid aptamer sandbox, LLM‑based agents can markedly improve hit rates through a lab‑in‑the‑loop approach, highlighting the pivotal role of experimental feedback in molecular discovery.