To successfully forage for food, animals much balance the energetic cost of searching for and traveling between food sources with the energetic benefit of exploiting those sources. The Marginal Value Theorem (MVT) provides one normative account of this balance by specifying that a forager should leave a food patch when its energetic yield falls below the average yield of other patches in the environment. This framework and its extensions treat the decision of when and how fast to leave a patch under the assumption that other patches exist and are readily reachable. However, in natural settings, a forager does not know whether it will encounter additional food patches, and must balance potential energetic costs and benefits accordingly. Here, we explore how a forager should structure its search for new food patches when (i) the existence of those patches is not known, and (ii) searching for those patches requires energy that can only be harvested from a single known food patch. Because the forager faces the possibility that there will not be any food patches nearby, we assume that it structures its search in a series of outbound and inbound trips to ensure that it returns to the known food patch if it fails to find a second patch. We identify conditions under which it is more favorable to explore the environment in several successive trips rather than one long exploration, and we show how the optimal sequence of trips depends on the forager's beliefs about the distribution and utility of food patches in the environment. Finally, we derive a local decision rule for structuring this search, and we show that this local rule can achieve near-optimal performance and be implemented by a simple neural circuit architecture. Together, this work highlights how energetic constraints shape optimal foraging strategies.