Can police search private property because they feel like it?

My family and I live in a suburban Rhode Island neighborhood, and at the end of my street is a gated beach area. It's around an acre of land with a small beach and a dock where my family keeps our boat. Earlier at around 9pm me and my Dad headed down to the boat to go out night fishing, and closed the entry gate behind us but did not lock it. The gate has a giant no trespassing sign and clearly states the property is private unless you are a part of the association. As me and my Dad are about to push off the dock on our boat, we see two police officers with flashlights searching the property. They eventually walk down the dock to our boat and start asking us questions such as what we are doing etc. We informed them that we are simply going out fishing and that this is private property. We asked if someone had called in a complaint and they said no, and claimed they are just "checking things out". One of the cops makes slightly snarky comments and asked where we live. We tell him we are not required to provide that information. Shortly after this they both leave after another search around the property. Are they allowed to search our property just because they feel like it? I know the gate was unlocked, but if the front door of my house was unlocked I certainly don't think police can just walk in because they want to "check things out". Is there anything we can do about this? Really don't need these random police searches of our property becoming a regular thing.